Dataset

Oklahoma Purchase Credit Card Transactions

The Office of Management and Enterprise Services in the State of Oklahoma has made its purchase credit card transactions available. This dataset contains information on purchases made through the purchase card programs administered by the state and higher education institutions.

Load Data

library(dplyr)
library(DataExplorer)
library(ggplot2)
library(plotly)
library(kableExtra)
library(reshape2)

#load data
ccard <- read.csv("res_purchase_card.csv")

Explore the DataFrame

#explore data
dim(ccard)
## [1] 442458     11
summary(ccard)
##    Year.Month     Agency.Number  
##  Min.   :201307   Min.   : 1000  
##  1st Qu.:201309   1st Qu.: 1000  
##  Median :201401   Median :47700  
##  Mean   :201357   Mean   :42786  
##  3rd Qu.:201404   3rd Qu.:76000  
##  Max.   :201406   Max.   :98000  
##                                  
##                                 Agency.Name    
##  OKLAHOMA STATE UNIVERSITY            :115995  
##  UNIVERSITY OF OKLAHOMA               : 76143  
##  UNIV. OF OKLA. HEALTH SCIENCES CENTER: 58247  
##  DEPARTMENT OF CORRECTIONS            : 22322  
##  DEPARTMENT OF TOURISM AND RECREATION : 17232  
##  DEPARTMENT OF TRANSPORTATION         : 15689  
##  (Other)                              :136830  
##                Cardholder.Last.Name Cardholder.First.Initial
##  JOURNEY HOUSE TRAVEL INC: 10137    J      : 55031          
##  UNIVERSITY AMERICAN     :  7219    G      : 42251          
##  JOURNEY HOUSE TRAVEL    :  4693    D      : 38120          
##  Heusel                  :  4212    M      : 35352          
##  Hines                   :  3423    S      : 34698          
##  Bowers                  :  2448    C      : 33213          
##  (Other)                 :410326    (Other):203793          
##                         Description         Amount         
##  GENERAL PURCHASE             :247187   Min.   : -42863.0  
##  AIR TRAVEL                   : 29584   1st Qu.:     30.9  
##  ROOM CHARGES                 : 18120   Median :    104.9  
##  AT&T SERVICE PAYMENT ITM     :  2657   Mean   :    425.0  
##  001 Priority          1LB PCE:  2005   3rd Qu.:    345.0  
##  000000000000000000000000     :  1828   Max.   :1903858.4  
##  (Other)                      :141077                      
##                        Vendor                     Transaction.Date 
##  STAPLES                  : 14842   09/11/2013 12:00:00 AM:  2122  
##  AMAZON MKTPLACE PMTS     : 12197   08/07/2013 12:00:00 AM:  2108  
##  WW GRAINGER              : 12076   01/14/2014 12:00:00 AM:  2059  
##  Amazon.com               : 10766   01/16/2014 12:00:00 AM:  2009  
##  BILL WARREN OFFICE PRODUC:  4479   09/05/2013 12:00:00 AM:  1999  
##  LOWES #00241             :  4231   10/01/2013 12:00:00 AM:  1996  
##  (Other)                  :383867   (Other)               :430165  
##                  Posted.Date    
##  01/13/2014 12:00:00 AM:  3256  
##  04/14/2014 12:00:00 AM:  3163  
##  03/10/2014 12:00:00 AM:  3139  
##  03/03/2014 12:00:00 AM:  3101  
##  09/16/2013 12:00:00 AM:  3062  
##  01/20/2014 12:00:00 AM:  3032  
##  (Other)               :423705  
##                                           Merchant.Category.Code..MCC.
##  STATIONERY, OFFICE SUPPLIES, PRINTING AND WRITING PAPER: 24860       
##  BOOK STORES                                            : 21981       
##  INDUSTRIAL SUPPLIES NOT ELSEWHERE CLASSIFIED           : 21669       
##  DENTAL/LABORATORY/MEDICAL/OPHTHALMIC HOSP EQIP AND SUP.: 20183       
##  GROCERY STORES,AND SUPERMARKETS                        : 17152       
##  MISCELLANEOUS AND SPECIALTY RETAIL STORES              : 13335       
##  (Other)                                                :323278
colnames(ccard)
##  [1] "Year.Month"                   "Agency.Number"               
##  [3] "Agency.Name"                  "Cardholder.Last.Name"        
##  [5] "Cardholder.First.Initial"     "Description"                 
##  [7] "Amount"                       "Vendor"                      
##  [9] "Transaction.Date"             "Posted.Date"                 
## [11] "Merchant.Category.Code..MCC."
nrow(ccard)
## [1] 442458
#change column names
colnames(ccard) <-
c(
'Year_Month',
'Agency_Number',
'Agency_Name',
'Cardholder_Last_Name',
'Cardholder_First_Initial',
'Description',
'Amount',
'Vendor',
'Transaction_Date',
'Posted_Date',
'Merchant_Category'
)

#view head of ccard
kable(head(ccard)) %>% kable_styling(latex_options = "scale_down")
Year_Month Agency_Number Agency_Name Cardholder_Last_Name Cardholder_First_Initial Description Amount Vendor Transaction_Date Posted_Date Merchant_Category
201307 1000 OKLAHOMA STATE UNIVERSITY Mason C GENERAL PURCHASE 890.00 NACAS 07/30/2013 12:00:00 AM 07/31/2013 12:00:00 AM CHARITABLE AND SOCIAL SERVICE ORGANIZATIONS
201307 1000 OKLAHOMA STATE UNIVERSITY Mason C ROOM CHARGES 368.96 SHERATON HOTEL 07/30/2013 12:00:00 AM 07/31/2013 12:00:00 AM SHERATON
201307 1000 OKLAHOMA STATE UNIVERSITY Massey J GENERAL PURCHASE 165.82 SEARS.COM 9300 07/29/2013 12:00:00 AM 07/31/2013 12:00:00 AM DIRCT MARKETING/DIRCT MARKETERS–NOT ELSEWHERE CLASSIFIED
201307 1000 OKLAHOMA STATE UNIVERSITY Massey T GENERAL PURCHASE 96.39 WAL-MART #0137 07/30/2013 12:00:00 AM 07/31/2013 12:00:00 AM GROCERY STORES,AND SUPERMARKETS
201307 1000 OKLAHOMA STATE UNIVERSITY Mauro-Herrera M HAMMERMILL COPY PLUS COPY EA 125.96 STAPLES DIRECT 07/30/2013 12:00:00 AM 07/31/2013 12:00:00 AM STATIONERY, OFFICE SUPPLIES, PRINTING AND WRITING PAPER
201307 1000 OKLAHOMA STATE UNIVERSITY Mauro-Herrera M GENERAL PURCHASE 394.28 KYOCERA DOCUMENT SOLUTION 07/29/2013 12:00:00 AM 07/31/2013 12:00:00 AM OFFICE, PHOTOGRAPHIC, PHOTOCOPY, AND MICROFILM EQUIPMENT 
#view count for each month
kable(table(ccard$Year_Month))
Var1 Freq
201307 37635
201308 39314
201309 38762
201310 40266
201311 34275
201312 26969
201401 37230
201402 35831
201403 38188
201404 39249
201405 36784
201406 37955

Feature Creation

Monetary Feature

#Add Monetary feature
#Add Max, Average and Median Amount Ratio Features by agency_name and merchant category
avg_agency <- ccard %>% group_by(Agency_Name, Merchant_Category) %>%
summarise(
mean_category_amount = mean(Amount),
median_category_amount = median(Amount),
mean_count_trans = n()
)
#view head of avg_agency
kable(head(avg_agency)) %>% kable_styling(latex_options = "scale_down")
Agency_Name Merchant_Category mean_category_amount median_category_amount mean_count_trans
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> ADVERTISING SERVICES </td> <td style="text-align:right;"> 508.48600 </td> <td style="text-align:right;"> 415.85 </td> <td style="text-align:right;"> 5 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION AMERICAN AIRLINES 492.98809 620.60 89
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> BEST WESTERN </td> <td style="text-align:right;"> 94.81143 </td> <td style="text-align:right;"> 83.00 </td> <td style="text-align:right;"> 7 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION BOOK STORES 131.82414 80.66 29
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> BOOKS, PERIODICALS AND NEWSPAPERS </td> <td style="text-align:right;"> 275.00000 </td> <td style="text-align:right;"> 275.00 </td> <td style="text-align:right;"> 1 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION BUSINESS SERVICES NOT ELSEWHERE CLASSIFIED 235.88067 300.00 15 
# Append the max, average and median statistics back to the data to derive the ratios.
# Select the most recent 4 transactions
per_agency_category <-
ccard %>% group_by(Agency_Name, Merchant_Category, Year_Month) %>%
summarise(
max_amount = max(Amount),
mean_amount = mean(Amount),
median_amount = median(Amount),
count_trans = n()
) %>%
left_join(avg_agency, by = c('Agency_Name', 'Merchant_Category')) %>%
mutate(
max_amount_ratio = max_amount / mean_category_amount,
mean_amount_ratio = mean_amount / mean_category_amount,
median_amount_ratio = median_amount / median_category_amount,
mean_count_ratio  = count_trans / mean_count_trans
) %>%
select(
-mean_category_amount,
-median_category_amount,
-mean_count_trans,-max_amount,
-mean_amount,
-median_amount,
-count_trans
) %>%
top_n(-4)  # Use top_n(xx) to select the top xx rows, and top_n(-xx) for the bottom xx rows

#summary
summary(per_agency_category)
##                                 Agency_Name   
##  OKLAHOMA STATE UNIVERSITY            : 1359  
##  UNIVERSITY OF OKLAHOMA               : 1080  
##  UNIV. OF OKLA. HEALTH SCIENCES CENTER:  749  
##  DEPARTMENT OF TOURISM AND RECREATION :  739  
##  DEPARTMENT OF CORRECTIONS            :  713  
##  GRAND RIVER DAM AUTH.                :  682  
##  (Other)                              :20764  
##                                                Merchant_Category
##  STATIONERY, OFFICE SUPPLIES, PRINTING AND WRITING PAPER:  438  
##  MISCELLANEOUS AND SPECIALTY RETAIL STORES              :  435  
##  BUSINESS SERVICES NOT ELSEWHERE CLASSIFIED             :  401  
##  GOVERNMENT SERVICES--NOT ELSEWHERE CLASSIFIED          :  381  
##  CHARITABLE AND SOCIAL SERVICE ORGANIZATIONS            :  363  
##  AMERICAN AIRLINES                                      :  350  
##  (Other)                                                :23718  
##    Year_Month     max_amount_ratio mean_amount_ratio median_amount_ratio
##  Min.   :201307   Min.   : -Inf    Min.   :  -Inf    Min.   :  -Inf     
##  1st Qu.:201310   1st Qu.:0.590    1st Qu.:0.4802    1st Qu.:0.7564     
##  Median :201401   Median :1.001    Median :0.9675    Median :1.0000     
##  Mean   :201357   Mean   :  NaN    Mean   :   NaN    Mean   :   NaN     
##  3rd Qu.:201404   3rd Qu.:1.899    3rd Qu.:1.2534    3rd Qu.:1.4870     
##  Max.   :201406   Max.   :  Inf    Max.   :   Inf    Max.   :   Inf     
##                                    NA's   :22        NA's   :22         
##  mean_count_ratio  
##  Min.   :0.002833  
##  1st Qu.:0.062500  
##  Median :0.111111  
##  Mean   :0.248170  
##  3rd Qu.:0.333333  
##  Max.   :1.000000  
## 
#some category summations equaled zero, resulted in INF ratio outputs, remove
per_agency_category <-
per_agency_category[is.finite(per_agency_category$max_amount_ratio),]

#view head of per_agency_category
kable(head(per_agency_category)) %>% kable_styling(latex_options = "scale_down")
Agency_Name Merchant_Category Year_Month max_amount_ratio mean_amount_ratio median_amount_ratio mean_count_ratio
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> ADVERTISING SERVICES </td> <td style="text-align:right;"> 201307 </td> <td style="text-align:right;"> 1.4822040 </td> <td style="text-align:right;"> 0.8296984 </td> <td style="text-align:right;"> 1.0000000 </td> <td style="text-align:right;"> 0.6000000 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION ADVERTISING SERVICES 201308 0.0749676 0.0749676 0.0916677 0.2000000
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> ADVERTISING SERVICES </td> <td style="text-align:right;"> 201401 </td> <td style="text-align:right;"> 2.4359373 </td> <td style="text-align:right;"> 2.4359373 </td> <td style="text-align:right;"> 2.9785740 </td> <td style="text-align:right;"> 0.2000000 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION AMERICAN AIRLINES 201307 1.7274251 1.4453020 1.1627457 0.1348315
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> AMERICAN AIRLINES </td> <td style="text-align:right;"> 201308 </td> <td style="text-align:right;"> 1.4637270 </td> <td style="text-align:right;"> 1.0760503 </td> <td style="text-align:right;"> 1.1627457 </td> <td style="text-align:right;"> 0.0561798 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION AMERICAN AIRLINES 201312 1.0986067 -0.1045326 0.1456655 0.0674157 
#create new DF, add Max to year_month column
max_per_agency_category <- per_agency_category %>%
mutate(Year_Month = paste("Max", Year_Month, sep = "_")) %>%
select(-mean_amount_ratio,-mean_count_ratio,-median_amount_ratio)

#view head of max_per_agency_category
kable(head(max_per_agency_category)) %>% kable_styling(latex_options = "scale_down")
Agency_Name Merchant_Category Year_Month max_amount_ratio
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> ADVERTISING SERVICES </td> <td style="text-align:left;"> Max_201307 </td> <td style="text-align:right;"> 1.4822040 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION ADVERTISING SERVICES Max_201308 0.0749676
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> ADVERTISING SERVICES </td> <td style="text-align:left;"> Max_201401 </td> <td style="text-align:right;"> 2.4359373 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION AMERICAN AIRLINES Max_201307 1.7274251
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> AMERICAN AIRLINES </td> <td style="text-align:left;"> Max_201308 </td> <td style="text-align:right;"> 1.4637270 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION AMERICAN AIRLINES Max_201312 1.0986067 
#create new DF, add Med to year_month column
med_per_agency_category <- per_agency_category %>%
mutate(Year_Month = paste("Med", Year_Month, sep = "_")) %>%
select(-mean_amount_ratio,-mean_count_ratio,-max_amount_ratio)

#view head of med_per_agency_category
kable(head(med_per_agency_category)) %>% kable_styling(latex_options = "scale_down")
Agency_Name Merchant_Category Year_Month median_amount_ratio
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> ADVERTISING SERVICES </td> <td style="text-align:left;"> Med_201307 </td> <td style="text-align:right;"> 1.0000000 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION ADVERTISING SERVICES Med_201308 0.0916677
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> ADVERTISING SERVICES </td> <td style="text-align:left;"> Med_201401 </td> <td style="text-align:right;"> 2.9785740 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION AMERICAN AIRLINES Med_201307 1.1627457
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> AMERICAN AIRLINES </td> <td style="text-align:left;"> Med_201308 </td> <td style="text-align:right;"> 1.1627457 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION AMERICAN AIRLINES Med_201312 0.1456655 
#create new DF, add Mean to year_month column
mean_per_agency_category <- per_agency_category %>%
mutate(Year_Month = paste("Mean", Year_Month, sep = "_")) %>%
select(-max_amount_ratio,-mean_count_ratio,-median_amount_ratio)

#view head of mean_per_agency_category
kable(head(mean_per_agency_category)) %>% kable_styling(latex_options = "scale_down")
Agency_Name Merchant_Category Year_Month mean_amount_ratio
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> ADVERTISING SERVICES </td> <td style="text-align:left;"> Mean_201307 </td> <td style="text-align:right;"> 0.8296984 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION ADVERTISING SERVICES Mean_201308 0.0749676
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> ADVERTISING SERVICES </td> <td style="text-align:left;"> Mean_201401 </td> <td style="text-align:right;"> 2.4359373 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION AMERICAN AIRLINES Mean_201307 1.4453020
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> AMERICAN AIRLINES </td> <td style="text-align:left;"> Mean_201308 </td> <td style="text-align:right;"> 1.0760503 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION AMERICAN AIRLINES Mean_201312 -0.1045326 
# Max variable: Use "dcast" in Library "reshape2" to organize the data so each row 
#is a merchant category of an agent.
max_wide <-
dcast(max_per_agency_category,
Agency_Name + Merchant_Category ~ Year_Month)
max_wide = as.matrix(max_wide)
max_wide[is.na(max_wide)] <- 0
max_wide = as.data.frame(max_wide)
#view head
kable(head(max_wide)) %>% kable_styling(latex_options = "scale_down")
Agency_Name Merchant_Category Max_201307 Max_201308 Max_201309 Max_201310 Max_201311 Max_201312 Max_201401 Max_201402 Max_201403 Max_201404 Max_201405 Max_201406
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> ADVERTISING SERVICES </td> <td style="text-align:left;"> 1.482204e+00 </td> <td style="text-align:left;"> 7.496765e-02 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 2.435937e+00 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION AMERICAN AIRLINES 1.727425e+00 1.463727e+00 0 0 0 1.098607e+00 1.127816e+00 0 0 0 0 0
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> BEST WESTERN </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 1.884583e+00 </td> <td style="text-align:left;"> 7.383076e-01 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 8.754219e-01 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION BOOK STORES 2.911303e+00 5.317691e-01 3.179236e-01 4.301184964 0 6.221167e-01 0 0 0 0 0 0
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> BOOKS, PERIODICALS AND NEWSPAPERS </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 1.000000000 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION BUSINESS SERVICES NOT ELSEWHERE CLASSIFIED 4.027460e-02 1.271830e+00 0 0 1.801759e+00 1.839701e+00 2.204505e+00 0 0 0 0 0 
# Median variable: Use "dcast" in Library "reshape2" to organize the data so each 
#row is a merchant category of an agent.
med_wide <-
dcast(med_per_agency_category,
Agency_Name + Merchant_Category ~ Year_Month)
med_wide = as.matrix(med_wide)
med_wide[is.na(med_wide)] <- 0
med_wide = as.data.frame(med_wide)
#view head
kable(head(med_wide)) %>% kable_styling(latex_options = "scale_down")
Agency_Name Merchant_Category Med_201307 Med_201308 Med_201309 Med_201310 Med_201311 Med_201312 Med_201401 Med_201402 Med_201403 Med_201404 Med_201405 Med_201406
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> ADVERTISING SERVICES </td> <td style="text-align:left;"> 1.000000e+00 </td> <td style="text-align:left;"> 9.166767e-02 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 2.978574e+00 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION AMERICAN AIRLINES 1.162746e+00 1.162746e+00 0 0 0 0.14566549 8.959072e-01 0 0 0 0 0
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> BEST WESTERN </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 2.152771e+00 </td> <td style="text-align:left;"> 8.433735e-01 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 1.000000e+00 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION BOOK STORES 8.430449e-01 8.690801e-01 5.195884e-01 1.640218200 0 0.72198116 0 0 0 0 0 0
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> BOOKS, PERIODICALS AND NEWSPAPERS </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 1.000000000 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION BUSINESS SERVICES NOT ELSEWHERE CLASSIFIED 3.166667e-02 1.881667e-01 0 0 1.416666667 1.38158333 5.000000e-01 0 0 0 0 0 
# Mean variable: Use "dcast" in Library "reshape2" to organize the data so each 
#row is a merchant category of an agent.
mean_wide <-
dcast(mean_per_agency_category,
Agency_Name + Merchant_Category ~ Year_Month)
mean_wide = as.matrix(mean_wide)
mean_wide[is.na(mean_wide)] <- 0
mean_wide = as.data.frame(mean_wide)
#view head
kable(head(mean_wide)) %>% kable_styling(latex_options = "scale_down")
Agency_Name Merchant_Category Mean_201307 Mean_201308 Mean_201309 Mean_201310 Mean_201311 Mean_201312 Mean_201401 Mean_201402 Mean_201403 Mean_201404 Mean_201405 Mean_201406
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> ADVERTISING SERVICES </td> <td style="text-align:left;"> 8.296984e-01 </td> <td style="text-align:left;"> 7.496765e-02 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 2.435937e+00 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION AMERICAN AIRLINES 1.445302e+00 1.076050e+00 0 0 0 -0.1045326132 8.628471e-01 0 0 0 0 0
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> BEST WESTERN </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 1.884583e+00 </td> <td style="text-align:left;"> 7.383076e-01 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 8.754219e-01 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION BOOK STORES 9.944309e-01 5.317691e-01 3.179236e-01 1.403551754 0 0.4417627979 0 0 0 0 0 0
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> BOOKS, PERIODICALS AND NEWSPAPERS </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 1.000000000 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION BUSINESS SERVICES NOT ELSEWHERE CLASSIFIED 4.027460e-02 5.065414e-01 0 0 1.8017585163 1.7571384966 9.489262e-01 0 0 0 0 0 
#merge dataframes
model_df_amt <-
left_join(max_wide, mean_wide, by = c('Agency_Name', 'Merchant_Category'))
model_df_amt <-
merge(model_df_amt,
med_wide,
by = c("Agency_Name", "Merchant_Category"))

Recency Feature

#Add Recency feature (time since last transaction) by agency_name and merchant category
#Add Max, Average and Median Recency Ratio Features by agency_name and merchant category
#create new DF grouped by agencies and by Merchant_Category,
#with Recency column
time_by_Merchant_Category <-
ccard %>% group_by(Agency_Name, Merchant_Category) %>%
mutate(Transaction_Date = as.Date(Transaction_Date, format = "%m/%d/%Y %H:%M")) %>%
arrange(Agency_Name, Merchant_Category, Transaction_Date) %>%
mutate(Recency = Transaction_Date - lag(Transaction_Date))

#view head of time_by_Merchant_Category
kable(head(time_by_Merchant_Category[, c("Agency_Number",
"Agency_Name",
"Merchant_Category",
"Transaction_Date",
"Recency")])) %>% kable_styling(latex_options = "scale_down")
Agency_Number Agency_Name Merchant_Category Transaction_Date Recency
26500 DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> ADVERTISING SERVICES </td> <td style="text-align:left;"> 2013-06-29 </td> <td style="text-align:left;"> NA </td> </tr> <tr> <td style="text-align:right;"> 26500 </td> <td style="text-align:left;">DEPARTMENT OF EDUCATION ADVERTISING SERVICES 2013-07-01 2 days
26500 DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> ADVERTISING SERVICES </td> <td style="text-align:left;"> 2013-07-12 </td> <td style="text-align:left;"> 11 days </td> </tr> <tr> <td style="text-align:right;"> 26500 </td> <td style="text-align:left;">DEPARTMENT OF EDUCATION ADVERTISING SERVICES 2013-08-01 20 days
26500 DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> ADVERTISING SERVICES </td> <td style="text-align:left;"> 2014-01-21 </td> <td style="text-align:left;"> 173 days </td> </tr> <tr> <td style="text-align:right;"> 26500 </td> <td style="text-align:left;">DEPARTMENT OF EDUCATION AMERICAN AIRLINES 2013-07-03 NA 
#sort by recency
Recency_cat_sorted <-
time_by_Merchant_Category %>% arrange(Merchant_Category, Recency) %>% na.omit

#Calculate the average and median recency by agency_name and merchant category
avg_recency <-
Recency_cat_sorted %>% group_by(Agency_Name, Merchant_Category) %>%
summarise(
mean_recency_amount = mean(Recency),
median_recency_amount = median(Recency),
mean_count_recency = n()
)
#view head of avg_recency
kable(head(avg_recency)) %>% kable_styling(latex_options = "scale_down")
Agency_Name Merchant_Category mean_recency_amount median_recency_amount mean_count_recency
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> ADVERTISING SERVICES </td> <td style="text-align:left;"> 51.50000 days </td> <td style="text-align:left;"> 15.5 days </td> <td style="text-align:right;"> 4 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION AMERICAN AIRLINES 2.37500 days 0.5 days 88
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> BEST WESTERN </td> <td style="text-align:left;"> 28.33333 days </td> <td style="text-align:left;"> 0.0 days </td> <td style="text-align:right;"> 6 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION BOOK STORES 6.50000 days 1.0 days 28
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> BUSINESS SERVICES NOT ELSEWHERE CLASSIFIED </td> <td style="text-align:left;"> 14.64286 days </td> <td style="text-align:left;"> 9.0 days </td> <td style="text-align:right;"> 14 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION CATALOG MERCHANTS 44.50000 days 44.5 days 2 
# Append the average and median recency statistics back to the data to derive the ratios.
# Select the most recent 4 transactions
per_agency_category_rec <-
Recency_cat_sorted %>% group_by(Agency_Name, Merchant_Category, Year_Month) %>%
summarise(
max_rec = max(Recency),
mean_rec = mean(Recency),
median_rec = median(Recency),
count_rec = n()
)

per_agency_category_rec <-
left_join(per_agency_category_rec,
avg_recency,
by = c('Agency_Name', 'Merchant_Category'))

#view class
lapply(per_agency_category_rec, class)
## $Agency_Name
## [1] "factor"
## 
## $Merchant_Category
## [1] "factor"
## 
## $Year_Month
## [1] "integer"
## 
## $max_rec
## [1] "difftime"
## 
## $mean_rec
## [1] "difftime"
## 
## $median_rec
## [1] "difftime"
## 
## $count_rec
## [1] "integer"
## 
## $mean_recency_amount
## [1] "difftime"
## 
## $median_recency_amount
## [1] "difftime"
## 
## $mean_count_recency
## [1] "integer"
#change all difftime columns to class numeric
per_agency_category_rec$max_rec <-
as.numeric(per_agency_category_rec$max_rec, units = "days")

per_agency_category_rec$mean_rec <-
as.numeric(per_agency_category_rec$mean_rec, units = "days")

per_agency_category_rec$median_rec <-
as.numeric(per_agency_category_rec$median_rec, units = "days")

per_agency_category_rec$mean_recency_amount <-
as.numeric(per_agency_category_rec$mean_recency_amount, units = "days")

per_agency_category_rec$median_recency_amount <-
as.numeric(per_agency_category_rec$median_recency_amount, units = "days")

#add ratios to per_agency_category_rec
per_agency_category_rec <- per_agency_category_rec %>%
mutate(
max_rec_ratio = max_rec / mean_recency_amount,
mean_rec_ratio = mean_rec / mean_recency_amount,
median_rec_ratio = median_rec / median_recency_amount,
mean_rec_ratio  = count_rec / mean_count_recency
) %>%
select(
-mean_recency_amount,
-median_recency_amount,
-mean_count_recency,-max_rec,
-mean_rec,
-median_rec,
-count_rec
) %>%
top_n(-4)  # Use top_n(xx) to select the top xx rows, and top_n(-xx) for the bottom xx rows

#remove INF from median_rec_ratio
per_agency_category_rec <-
per_agency_category_rec[is.finite(per_agency_category_rec$median_rec_ratio),]

#create new DF, add MaxR to year_month column
max_per_agency_categor_rec <- per_agency_category_rec %>%
mutate(Year_Month = paste("MaxR", Year_Month, sep = "_")) %>%
select(-mean_rec_ratio,-median_rec_ratio)

#view head of max_per_agency_category_rec
kable(head(max_per_agency_categor_rec)) %>% kable_styling(latex_options = "scale_down")
Agency_Name Merchant_Category Year_Month max_rec_ratio
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> ADVERTISING SERVICES </td> <td style="text-align:left;"> MaxR_201307 </td> <td style="text-align:right;"> 0.2135922 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION ADVERTISING SERVICES MaxR_201308 0.3883495
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> ADVERTISING SERVICES </td> <td style="text-align:left;"> MaxR_201401 </td> <td style="text-align:right;"> 3.3592233 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION AMERICAN AIRLINES MaxR_201307 2.9473684
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> AMERICAN AIRLINES </td> <td style="text-align:left;"> MaxR_201309 </td> <td style="text-align:right;"> 3.3684211 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION AMERICAN AIRLINES MaxR_201310 4.6315789 
#create new DF, add MedR to year_month column
med_per_agency_category_rec <- per_agency_category_rec %>%
mutate(Year_Month = paste("MedR", Year_Month, sep = "_")) %>%
select(-mean_rec_ratio,-max_rec_ratio)

#view head of med_per_agency_category_rec
kable(head(med_per_agency_category_rec)) %>% kable_styling(latex_options = "scale_down")
Agency_Name Merchant_Category Year_Month median_rec_ratio
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> ADVERTISING SERVICES </td> <td style="text-align:left;"> MedR_201307 </td> <td style="text-align:right;"> 0.4193548 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION ADVERTISING SERVICES MedR_201308 1.2903226
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> ADVERTISING SERVICES </td> <td style="text-align:left;"> MedR_201401 </td> <td style="text-align:right;"> 11.1612903 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION AMERICAN AIRLINES MedR_201307 2.0000000
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> AMERICAN AIRLINES </td> <td style="text-align:left;"> MedR_201309 </td> <td style="text-align:right;"> 0.0000000 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION AMERICAN AIRLINES MedR_201310 2.0000000 
#create new DF, add MeanR to year_month column
mean_per_agency_category_rec <- per_agency_category_rec %>%
mutate(Year_Month = paste("MeanR", Year_Month, sep = "_")) %>%
select(-median_rec_ratio,-max_rec_ratio)

#view head of mean_per_agency_category_rec
kable(head(mean_per_agency_category_rec)) %>% kable_styling(latex_options = "scale_down")
Agency_Name Merchant_Category Year_Month mean_rec_ratio
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> ADVERTISING SERVICES </td> <td style="text-align:left;"> MeanR_201307 </td> <td style="text-align:right;"> 0.5000000 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION ADVERTISING SERVICES MeanR_201308 0.2500000
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> ADVERTISING SERVICES </td> <td style="text-align:left;"> MeanR_201401 </td> <td style="text-align:right;"> 0.2500000 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION AMERICAN AIRLINES MeanR_201307 0.1250000
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> AMERICAN AIRLINES </td> <td style="text-align:left;"> MeanR_201309 </td> <td style="text-align:right;"> 0.2500000 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION AMERICAN AIRLINES MeanR_201310 0.2727273 
#Max Recency variable: Use "dcast" in Library "reshape2" to organize the data 
#so each row is a merchant category of an agent.
max_wide_rec <-
dcast(max_per_agency_categor_rec,
Agency_Name + Merchant_Category ~ Year_Month)
max_wide_rec = as.matrix(max_wide_rec)
max_wide_rec[is.na(max_wide_rec)] <- 0
max_wide_rec = as.data.frame(max_wide_rec)
#view head
kable(head(max_wide_rec)) %>% kable_styling(latex_options = "scale_down")
Agency_Name Merchant_Category MaxR_201307 MaxR_201308 MaxR_201309 MaxR_201310 MaxR_201311 MaxR_201312 MaxR_201401 MaxR_201402 MaxR_201403 MaxR_201404 MaxR_201405 MaxR_201406
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> ADVERTISING SERVICES </td> <td style="text-align:left;"> 0.21359223 </td> <td style="text-align:left;"> 0.38834951 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 3.35922330 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION AMERICAN AIRLINES 2.94736842 0 3.368421053 4.631578947 6.31578947 0 0 0 0 0 0 0
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> BOOK STORES </td> <td style="text-align:left;"> 2.00000000 </td> <td style="text-align:left;"> 0.61538462 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 4.769230769 </td> <td style="text-align:left;"> 1.23076923 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION BUSINESS SERVICES NOT ELSEWHERE CLASSIFIED 0 2.04878049 1.365853659 0 0 2.66341463 0.95609756 0 0 0 0 0
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> CATALOG MERCHANTS </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 1.595505618 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION CHARITABLE AND SOCIAL SERVICE ORGANIZATIONS 0 1.95348837 1.395348837 2.372093023 0 5.44186047 0 0 0 0 0 0 
# Median Recency variable: Use "dcast" in Library "reshape2" to organize the 
#data so each row is a merchant category of an agent.
med_wide_rec <-
dcast(med_per_agency_category_rec,
Agency_Name + Merchant_Category ~ Year_Month)
med_wide_rec = as.matrix(med_wide_rec)
med_wide_rec[is.na(med_wide_rec)] <- 0
med_wide_rec = as.data.frame(med_wide_rec)
#view head
kable(head(med_wide_rec)) %>% kable_styling(latex_options = "scale_down")
Agency_Name Merchant_Category MedR_201307 MedR_201308 MedR_201309 MedR_201310 MedR_201311 MedR_201312 MedR_201401 MedR_201402 MedR_201403 MedR_201404 MedR_201405 MedR_201406
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> ADVERTISING SERVICES </td> <td style="text-align:left;"> 0.41935484 </td> <td style="text-align:left;"> 1.29032258 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 11.16129032 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION AMERICAN AIRLINES 2.00000000 0 0.000000000 2.000000000 0.00000000 0 0 0 0 0 0 0
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> BOOK STORES </td> <td style="text-align:left;"> 7.00000000 </td> <td style="text-align:left;"> 4.00000000 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 4.000000000 </td> <td style="text-align:left;"> 0.00000000 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION BUSINESS SERVICES NOT ELSEWHERE CLASSIFIED 0 1.77777778 0.555555556 0 0 2.33333333 1.11111111 0 0 0 0 0
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> CATALOG MERCHANTS </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 1.000000000 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION CHARITABLE AND SOCIAL SERVICE ORGANIZATIONS 0 0.50000000 1.000000000 1.000000000 0 1.25000000 0 0 0 0 0 0 
# Mean Recency variable: Use "dcast" in Library "reshape2" to organize the 
#data so each row is a merchant category of an agent.
mean_wide_rec <-
dcast(mean_per_agency_category_rec,
Agency_Name + Merchant_Category ~ Year_Month)
mean_wide_rec = as.matrix(mean_wide_rec)
mean_wide_rec[is.na(mean_wide_rec)] <- 0
mean_wide_rec = as.data.frame(mean_wide_rec)
#view head
kable(head(mean_wide_rec)) %>% kable_styling(latex_options = "scale_down")
Agency_Name Merchant_Category MeanR_201307 MeanR_201308 MeanR_201309 MeanR_201310 MeanR_201311 MeanR_201312 MeanR_201401 MeanR_201402 MeanR_201403 MeanR_201404 MeanR_201405 MeanR_201406
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> ADVERTISING SERVICES </td> <td style="text-align:left;"> 0.50000000 </td> <td style="text-align:left;"> 0.25000000 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0.25000000 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION AMERICAN AIRLINES 0.12500000 0 0.25000000 0.27272727 0.15909091 0 0 0 0 0 0 0
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> BOOK STORES </td> <td style="text-align:left;"> 0.14285714 </td> <td style="text-align:left;"> 0.03571429 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0.17857143 </td> <td style="text-align:left;"> 0.53571429 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION BUSINESS SERVICES NOT ELSEWHERE CLASSIFIED 0 0.21428571 0.35714286 0 0 0.14285714 0.21428571 0 0 0 0 0
DEPARTMENT OF EDUCATION </td> <td style="text-align:left;"> CATALOG MERCHANTS </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 1.00000000 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> <td style="text-align:left;"> 0 </td> </tr> <tr> <td style="text-align:left;">DEPARTMENT OF EDUCATION CHARITABLE AND SOCIAL SERVICE ORGANIZATIONS 0 0.33333333 0.25000000 0.25000000 0 0.12500000 0 0 0 0 0 0 
#merge dataframes
model_df_rec <-
left_join(max_wide_rec,
mean_wide_rec,
by = c('Agency_Name', 'Merchant_Category'))
model_df_rec <-
merge(model_df_rec,
med_wide_rec,
by = c("Agency_Name", "Merchant_Category"))

#merge recency and transaction amount dataframes
model_df <-
merge(model_df_amt,
model_df_rec,
by = c("Agency_Name", "Merchant_Category"))

#View in excel, write to CSV
#write_csv(model_df, "model_df.csv")

#remove identifier columns
#model_df$Agency_Name <- NULL
#model_df$Merchant_Category <- NULL

#change ratio columns to numeric
cols = c(3:74)
model_df[, cols] = apply(model_df[, cols], 2, function(x)
as.numeric(as.character(x)))

#scale data
model_df_scale <- as.data.frame(scale(model_df[, cols]))

#remove mean ratio calculations, use median as a feature instead as 
#it is not impacted by outliers.
to.remove <-
c(
"Mean_201307",
"Mean_201308",
"Mean_201309",
"Mean_201310",
"Mean_201311",
"Mean_201312",
"Mean_201401",
"Mean_201402",
"Mean_201403",
"Mean_201404",
"Mean_201405",
"Mean_201406",
"MeanR_201307",
"MeanR_201308",
"MeanR_201309",
"MeanR_201310",
"MeanR_201311",
"MeanR_201312",
"MeanR_201401",
"MeanR_201402",
"MeanR_201403",
"MeanR_201404",
"MeanR_201405",
"MeanR_201406"
)
`%ni%` <- Negate(`%in%`)
model_df_scale <-
subset(model_df_scale, select = names(model_df_scale) %ni% to.remove)

DBSCAN Modeling Technique

DBCAN Method

DBSCAN is a density based clustering algorithm. Unlike K-means, which makes round clusters, DBSCAN can handle clusters of various shapes and sizes. It is therefore able to find clusters that K-means is unable to discover. For fraud analysis, DBSCAN will group together points that are closely packed together and mark outlier points that lie outside these clusters. These outlier points could be possible fraudulent transactions.

DBSCAN Model

Hyperparameters tuned include:

minPts - how many neighbors a point should have to be included into a cluster

eps (epsilon) - how close points should be to each other to be considered a part of a cluster

#load library
library(dbscan)
library(fpc)
library(factoextra)
library(rattle.data)

#principal component anlaysis to reduce high-dimensional data to two dimensions
fraud_PCA <- prcomp(model_df_scale)
fraud_PCA2 <- fraud_PCA$x[, 1:2]

#view head of ccard
kable(head(fraud_PCA2))
PC1 PC2
0.6956969 0.2121071
-4.1154660 0.1033287
-5.1863068 0.3878899
-0.3590404 0.1282656
1.2587429 0.1550933
-1.5495084 0.0768009 
#Compute DBSCAN using fpc package
#minPts
#The rule of thumb for minPts is to use at least the number of dimensions of the data set plus one.
#(source: https://cran.r-project.org/web/packages/dbscan/vignettes/dbscan.pdf)
#In our case, this is 3.  However, I tested other MinPts as well.
#I tested 3, 5, 20, 50 and 100.

#eps
#For eps, we can plot the points’ kNN distances (i.e., the distance to the kth nearest neighbor)
#in decreasing order and look for a knee in the plot.
#(source: https://cran.r-project.org/web/packages/dbscan/vignettes/dbscan.pdf)

#minPts = 3
kNNdistplot(model_df_scale, k = 3)
abline(h = 12, col = "red", lty = 2) #EPS = 12

#minPts = 5
kNNdistplot(model_df_scale, k = 5)
abline(h = 12, col = "red", lty = 2) #EPS = 12

#minPts = 20
kNNdistplot(model_df_scale, k = 20)
abline(h = 15, col = "red", lty = 2) #EPS = 15

#minPts = 50
kNNdistplot(model_df_scale, k = 50)
abline(h = 15, col = "red", lty = 2) #EPS = 15

#minPts = 100
kNNdistplot(model_df_scale, k = 100)
abline(h = 15, col = "red", lty = 2) #EPS = 15

#eps = 12, MinPts = 3
set.seed(1)
modl <- fpc::dbscan(model_df_scale, eps = 12, MinPts = 3)
#view table
modl #The clustering contains 3 clusters and 52 noise points.
## dbscan Pts=5471 MinPts=3 eps=12
##         0    1 2 3
## border 52   10 0 0
## seed    0 5401 3 5
## total  52 5411 3 5
#plot clusters and add noise (cluster 0) as crosses.
plot(
fraud_PCA2,
main = "Credit Card Transaction Clusters\neps = 12, MinPts = 3",
sub = "Noise points plotted as crosses",
cex.sub = 0.75,
font.sub = 3,
col.sub = "red",
col =
modl$cluster
)
points(fraud_PCA2[modl$cluster == 0,], pch = 3, col = "red")

noise <- model_df[modl$cluster == 0,]

#eps = 12, MinPts = 5
set.seed(1)
modl2 <- fpc::dbscan(model_df_scale, eps = 12, MinPts = 5)
#view table
modl2 #The clustering contains 2 clusters and 58 noise points.
## dbscan Pts=5471 MinPts=5 eps=12
##         0    1 2
## border 58   25 0
## seed    0 5383 5
## total  58 5408 5
#plot clusters and add noise (cluster 0) as crosses.
plot(
fraud_PCA2,
main = "Credit Card Transaction Clusters\neps = 12, MinPts = 5",
sub = "Noise points plotted as crosses",
cex.sub = 0.75,
font.sub = 3,
col.sub = "red",
col =
modl2$cluster
)
points(fraud_PCA2[modl2$cluster == 0,], pch = 3, col = "red")

noise <- model_df[modl2$cluster == 0,]

#eps = 15, MinPts = 20
set.seed(1)
modl2b <- fpc::dbscan(model_df_scale, eps = 15, MinPts = 20)
#view table
modl2b #The clustering contains 1 cluster and 44 noise points.
## dbscan Pts=5471 MinPts=20 eps=15
##         0    1
## border 44   44
## seed    0 5383
## total  44 5427
#plot clusters and add noise (cluster 0) as crosses.
plot(
fraud_PCA2,
main = "Credit Card Transaction Clusters\neps = 15, MinPts = 20",
sub = "Noise points plotted as crosses",
cex.sub = 0.75,
font.sub = 3,
col.sub = "red",
col =
modl2b$cluster
)
points(fraud_PCA2[modl2b$cluster == 0,], pch = 3, col = "red")

noise <- model_df[modl2b$cluster == 0,]

#eps = 15, MinPts = 50
set.seed(1)
modl3 <- fpc::dbscan(model_df_scale, eps = 15, MinPts = 50)
#view table
modl3 #The clustering contains 1 cluster and 46 noise points.
## dbscan Pts=5471 MinPts=50 eps=15
##         0    1
## border 46   57
## seed    0 5368
## total  46 5425
#plot clusters and add noise (cluster 0) as crosses.
plot(
fraud_PCA2,
main = "Credit Card Transaction Clusters\neps = 15, MinPts = 50",
sub = "Noise points plotted as crosses",
cex.sub = 0.75,
font.sub = 3,
col.sub = "red",
col =
modl3$cluster
)
points(fraud_PCA2[modl3$cluster == 0,], pch = 3, col = "red")

noise <- model_df[modl3$cluster == 0,]

#eps = 15, MinPts = 100
set.seed(1)
modl4 <- fpc::dbscan(model_df_scale, eps = 15, MinPts = 100)
#view table
modl4 #The clustering contains 1 cluster and 46 noise points.
## dbscan Pts=5471 MinPts=100 eps=15
##         0    1
## border 46   67
## seed    0 5358
## total  46 5425
#plot clusters and add noise (cluster 0) as crosses.
plot(
fraud_PCA2,
main = "Credit Card Transaction Clusters\neps = 15, MinPts = 100",
sub = "Noise points plotted as crosses",
cex.sub = 0.75,
font.sub = 3,
col.sub = "red",
col =
modl4$cluster
)
points(fraud_PCA2[modl4$cluster == 0,], pch = 3, col = "red")

noise <- model_df[modl4$cluster == 0,]

#I also tested smaller numbers for EPS - 0.01, 0.15, 0.5, 0.99, 2.0
#eps = .01, MinPts = 50
set.seed(1)
modl5 <- fpc::dbscan(model_df_scale, eps = 0.01, MinPts = 50)
#view table
modl5 #The clustering contains 0 clusters and 5471 noise points, not useful.
## dbscan Pts=5471 MinPts=50 eps=0.01
## 
##    0 
## 5471
#plot clusters and add noise (cluster 0) as crosses.
plot(
fraud_PCA2,
main = "Credit Card Transaction Clusters\neps = .01, MinPts = 50",
sub = "Noise points plotted as crosses",
cex.sub = 0.75,
font.sub = 3,
col.sub = "red",
col =
modl5$cluster
)
points(fraud_PCA2[modl5$cluster == 0,], pch = 3, col = "red")

noise <- model_df[modl5$cluster == 0,]

#eps = 0.15, MinPts = 50
set.seed(1)
modl6 <- fpc::dbscan(model_df_scale, eps = 0.15, MinPts = 50)
#view table
modl6 #The clustering contains 0 clusters and 5471 noise points, not useful.
## dbscan Pts=5471 MinPts=50 eps=0.15
## 
##    0 
## 5471
#plot clusters and add noise (cluster 0) as crosses.
plot(
fraud_PCA2,
main = "Credit Card Transaction Clusters\neps = .15, MinPts = 50",
sub = "Noise points plotted as crosses",
cex.sub = 0.75,
font.sub = 3,
col.sub = "red",
col =
modl6$cluster
)
points(fraud_PCA2[modl6$cluster == 0,], pch = 3, col = "red")

noise <- model_df[modl6$cluster == 0,]

#eps = 0.5, MinPts = 50
set.seed(1)
modl7 <- fpc::dbscan(model_df_scale, eps = 0.5, MinPts = 50)
#view table
modl7 #The clustering contains 3 clusters and 5265 noise points, not useful.
## dbscan Pts=5471 MinPts=50 eps=0.5
##           0  1  2  3
## border 5265 41 60 51
## seed      0 26 16 12
## total  5265 67 76 63
#plot clusters and add noise (cluster 0) as crosses.
plot(
fraud_PCA2,
main = "Credit Card Transaction Clusters\neps = .5, MinPts = 50",
sub = "Noise points plotted as crosses",
cex.sub = 0.75,
font.sub = 3,
col.sub = "red",
col =
modl7$cluster
)
points(fraud_PCA2[modl7$cluster == 0,], pch = 3, col = "red")

noise <- model_df[modl7$cluster == 0,]

#eps = 0.99, MinPts = 50
set.seed(1)
modl8 <- fpc::dbscan(model_df_scale, eps = 0.99, MinPts = 50)
#view table
modl8 #The clustering contains 8 clusters and 4289 noise points, not useful.
## dbscan Pts=5471 MinPts=50 eps=0.99
##           0  1  2   3  4   5   6  7   8
## border 4289 35 48  42 37 101 122 39  50
## seed      0 43 46  77 27 146 232 57  80
## total  4289 78 94 119 64 247 354 96 130
#plot clusters and add noise (cluster 0) as crosses.
plot(
fraud_PCA2,
main = "Credit Card Transaction Clusters\neps = .5, MinPts = 50",
sub = "Noise points plotted as crosses",
cex.sub = 0.75,
font.sub = 3,
col.sub = "red",
col =
modl8$cluster
)
points(fraud_PCA2[modl8$cluster == 0,], pch = 3, col = "red")

noise <- model_df[modl8$cluster == 0,]

#eps = 2, MinPts = 50
set.seed(1)
modl9 <- fpc::dbscan(model_df_scale, eps = 2, MinPts = 50)
#view table
modl9 #The clustering contains 1 cluster1 and 2633 noise points, not useful.
## dbscan Pts=5471 MinPts=50 eps=2
##           0    1
## border 2633  827
## seed      0 2011
## total  2633 2838
#plot clusters and add noise (cluster 0) as crosses.
plot(
fraud_PCA2,
main = "Credit Card Transaction Clusters\neps = 2, MinPts = 50",
sub = "Noise points plotted as crosses",
cex.sub = 0.75,
font.sub = 3,
col.sub = "red",
col =
modl9$cluster
)
points(fraud_PCA2[modl9$cluster == 0,], pch = 3, col = "red")

noise <- model_df[modl9$cluster == 0,]

Best Model with hyperparameters of MinPts=50 and eps=15

It appears that using eps of 15 and MinPts of 50 resulted in a reasonable model. It clustered the data points into 1 cluster with 46 outliers.

modl3 #The clustering contains 1 cluster and 46 noise points.
## dbscan Pts=5471 MinPts=50 eps=15
##         0    1
## border 46   57
## seed    0 5368
## total  46 5425
#plot clusters and add noise (cluster 0) as crosses.
plot(fraud_PCA2, main = "Credit Card Transaction Clusters\neps = 15, MinPts = 50", sub = "Noise points plotted as crosses", cex.sub = 0.75, font.sub = 3, col.sub = "red", col =
modl3$cluster)
points(fraud_PCA2[modl3$cluster == 0, ], pch = 3, col = "red")

noise <- model_df[modl3$cluster == 0, ]

Anomalies

#create DF that include possible fraud transactions
fraud <- model_df[modl3$cluster == 0, ]
fraud <- fraud[, 1:2]

#view fraud
kable(fraud) %>% kable_styling(latex_options = "scale_down")
Agency_Name Merchant_Category
35 ARDMORE HIGHER EDUCATION CENTER HOUSEHOLD APPLIANCE STORES
279 COMM. ON CONSUMER CREDIT GOVERNMENT SERVICES–NOT ELSEWHERE CLASSIFIED
293 COMM. ON CONSUMER CREDIT SHERATON
327 COMPSOURCE OKLAHOMA DELTA
1301 DEPARTMENT OF REHABILITATION SERVICES GOVERNMENT SERVICES–NOT ELSEWHERE CLASSIFIED
1328 DEPARTMENT OF REHABILITATION SERVICES MISCELLANEOUS FOOD STORES-CONV STRS AND SPECIALTY MKTS.
1462 DEPARTMENT OF TOURISM AND RECREATION MISCELLANEOUS AND SPECIALTY RETAIL STORES
1495 DEPARTMENT OF TOURISM AND RECREATION SHERATON
1542 DEPARTMENT OF TRANSPORTATION COMMERCIAL EQUIPMENT, NOT ELSEWHERE CLASSIFIED
1721 DEPARTMENT OF VETERANS AFFAIRS MARRIOTT
1826 DEPARTMENT OF WILDLIFE CONSERVATION HILTON HOTELS
2159 GRAND RIVER DAM AUTH. COMMERCIAL EQUIPMENT, NOT ELSEWHERE CLASSIFIED
2165 GRAND RIVER DAM AUTH. COMPUTERS, COMPUTER PERIPHERAL EQUIPMENT, SOFTWARE
2174 GRAND RIVER DAM AUTH. DETECTIVE AGENCIES,PROTECTIVE AGENCIES,AND SECURITY SERVICES
2182 GRAND RIVER DAM AUTH. EMPLOYMENT AGENCIES AND TEMPORARY HELP SERVICES
2194 GRAND RIVER DAM AUTH. GOVERNMENT SERVICES–NOT ELSEWHERE CLASSIFIED
2203 GRAND RIVER DAM AUTH. HOMEWOOD SUITES
2260 GRAND RIVER DAM AUTH. TELECOMMUNICATION EQUIPMENT AND TELEPHONE SALES
2614 MENTAL HEALTH AND SUBSTANCE ABUSE SERV. DEPARTMENT STORES
2687 MENTAL HEALTH AND SUBSTANCE ABUSE SERV. RENAISSANCE HOTELS
2713 N. E. OKLA. A & M COLLEGE AUTOMATED FUEL DISPENSER
2752 N. E. OKLA. A & M COLLEGE RECORD STORES
2782 OFFICE OF JUVENILE AFFAIRS COMFORT HOTEL INTERNATIONAL
2865 OFFICE OF MANAGEMENT AND ENTERPRISE SERV BUSINESS SERVICES NOT ELSEWHERE CLASSIFIED
2880 OFFICE OF MANAGEMENT AND ENTERPRISE SERV COMMERCIAL EQUIPMENT, NOT ELSEWHERE CLASSIFIED
2975 OFFICE OF MANAGEMENT AND ENTERPRISE SERV TOLLS AND BRIDGE FEES
3330 OKLA. CITY COMMUNITY COLLEGE GROCERY STORES,AND SUPERMARKETS
3374 OKLA. HORSE RACING COMM. GOVERNMENT SERVICES–NOT ELSEWHERE CLASSIFIED
3471 OKLA. PANHANDLE STATE UNIV. MOTOR FREIGHT CARRIERS,AND TRUCKING
3485 OKLA. PANHANDLE STATE UNIV. RECORD STORES
3572 OKLAHOMA AERONAUTICS COMMISSION COMP PROG,DATA PROCESSING,AND INTEGRATED SYS DES IGN SVCS
3821 OKLAHOMA STATE UNIVERSITY AIRLINES AND AIR CARRIERS
3937 OKLAHOMA STATE UNIVERSITY LOCAL AND SUBURBAN COMMUTER PASS TRANS, INCLUDING FEE
3988 OKLAHOMA STATE UNIVERSITY RECORD STORES
4022 OKLAHOMA STATE UNIVERSITY VARIETY STORES
4143 REDLANDS COMMUNITY COLLEGE COLLEGES,UNIVERSITIES,PROFESSIONAL SCHLS AND JR COLLEGES
4165 REDLANDS COMMUNITY COLLEGE LUXOR HOTEL AND CASINO
4450 SECRETARY OF STATE TRAVEL AGENCIES
4699 STATE DEPARTMENT OF HEALTH HYATT PLACE
4713 STATE DEPARTMENT OF HEALTH MISCELLANEOUS GENERAL MERCHANDISE
4717 STATE DEPARTMENT OF HEALTH NON-DURABLE GOODS NOT ELSEWHERE CLASSIFIED
4752 STATE ELECTION BOARD STATIONERY,OFFICE AND SCHOOL SUPPLY STORES
4993 TULSA COMMUNITY COLLEGE NON-DURABLE GOODS NOT ELSEWHERE CLASSIFIED
5156 UNIV.OF SCIENCE & ARTS OF OK COMFORT HOTEL INTERNATIONAL
5169 UNIV.OF SCIENCE & ARTS OF OK FAST FOOD RESTAURANTS
5239 UNIVERSITY OF OKLAHOMA CAMPER,RECREATIONAL AND UTILITY TRAILER DEALERS

Business Insight

Agency transactions that occurred within the merchant category listed in the fraud data frame could possibly be fraud based on my DBSCAN analysis. Transactions that occurred within these merchant categories at these agencies require further analysis to determine if fraud actually occurred.

MeanShift Modeling Technique

MeanShift Method

The mean shift algorithm is a non parametric clustering technique. It can handle clusters of various shapes and sizes and prior knowledge of the number of clusters is not required. For each data point, mean shift defines a window around it and computes the mean of the data point. It then shifts the center of the window towards the mean and repeats the algorithm until it converges. For fraud analysis, data points far from the centroids can be ignored by the clustering process and flagged as anomalies. These anomaly points could be possible fraudulent transactions.

MeanShift Model

Hyperparameter tuned include: h: a positive bandwidth parameter. Larger values of h produce few and large clusters. Smaller values of h produce many small clusters.

I analyzed h values of: 10, 20, 30, 50 and 75.

#load library
library(MeanShift)
library(ggfortify)

#view dimension of model_df_scale
dim(model_df_scale)
## [1] 5471   48
#transpose data
model_df_trans <- t(model_df_scale)

#view dimension of model_df_trans
dim(model_df_trans)
## [1]   48 5471
#view head of model_df_trans
kable(head(model_df_trans))
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 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#H = 10.0
#MeanShift clustering using multi-core processing
options(mc.cores = 2)
ms_clustering <-
msClustering(model_df_trans, h = 10.0, multi.core = TRUE)

#attach clustering labels to model df
model_ms <- model_df
model_ms[, 'ms_label'] <- ms_clustering[2]

#change labels to factors
model_ms[, 'ms_label'] <- as.factor(model_ms[, 'ms_label'])

#view factor levels of ms_label column
levels(model_ms$ms_label)
##  [1] "1"  "2"  "3"  "4"  "5"  "6"  "7"  "8"  "9"  "10" "11" "12" "13" "14"
## [15] "15" "16" "17" "18" "19" "20" "21" "22" "23" "24" "25" "26" "27" "28"
## [29] "29" "30" "31" "32" "33" "34" "35" "36" "37" "38" "39" "40" "41" "42"
## [43] "43" "44" "45" "46" "47" "48" "49" "50" "51" "52" "53" "54" "55" "56"
## [57] "57" "58" "59" "60" "61" "62" "63" "64" "65" "66" "67" "68" "69" "70"
## [71] "71" "72" "73" "74" "75" "76" "77" "78" "79" "80" "81" "82" "83" "84"
## [85] "85"
#view number of occurances per factor level
model_ms %>%
group_by(ms_label) %>%
summarise(no_rows = length(ms_label)) #cluster 1 has 5377 data points, cluster 2 has 3 data points,cluster 3 has 2 data points and clusters 4-85 have one point each.
## # A tibble: 85 x 2
##    ms_label no_rows
##      <fctr>   <int>
##  1        1    5377
##  2        2       3
##  3        3       2
##  4        4       1
##  5        5       1
##  6        6       1
##  7        7       1
##  8        8       1
##  9        9       1
## 10       10       1
## # ... with 75 more rows
#plot using principal component anlaysis to reduce high-dimensional data to two dimensions
autoplot(
prcomp(model_ms[, 3:12], center = TRUE, scale. = TRUE),
data = model_ms,
colour = 'ms_label',
frame = TRUE
)

#H = 20.0
#MeanShift clustering using multi-core processing
options(mc.cores = 2)
ms_clustering <-
msClustering(model_df_trans, h = 20.0, multi.core = TRUE)

#attach clustering labels to model df
model_ms <- model_df
model_ms[, 'ms_label'] <- ms_clustering[2]

#change labels to factors
model_ms[, 'ms_label'] <- as.factor(model_ms[, 'ms_label'])

#view factor levels of ms_label column
levels(model_ms$ms_label)
##  [1] "1"  "2"  "3"  "4"  "5"  "6"  "7"  "8"  "9"  "10" "11" "12" "13" "14"
## [15] "15" "16" "17" "18" "19" "20" "21" "22" "23"
#view number of occurances per factor level
model_ms %>%
group_by(ms_label) %>%
summarise(no_rows = length(ms_label)) #cluster 1 has 5449 data points, clusters 2-23 have one point each.
## # A tibble: 23 x 2
##    ms_label no_rows
##      <fctr>   <int>
##  1        1    5449
##  2        2       1
##  3        3       1
##  4        4       1
##  5        5       1
##  6        6       1
##  7        7       1
##  8        8       1
##  9        9       1
## 10       10       1
## # ... with 13 more rows
#plot using principal component anlaysis to reduce high-dimensional data to two dimensions
autoplot(
prcomp(model_ms[, 3:12], center = TRUE, scale. = TRUE),
data = model_ms,
colour = 'ms_label',
frame = TRUE
)

#H = 30.0
#MeanShift clustering using multi-core processing
options(mc.cores = 2)
ms_clustering <-
msClustering(model_df_trans, h = 30.0, multi.core = TRUE)

#attach clustering labels to model df
model_ms <- model_df
model_ms[, 'ms_label'] <- ms_clustering[2]

#change labels to factors
model_ms[, 'ms_label'] <- as.factor(model_ms[, 'ms_label'])

#view factor levels of ms_label column
levels(model_ms$ms_label)
##  [1] "1"  "2"  "3"  "4"  "5"  "6"  "7"  "8"  "9"  "10" "11" "12" "13" "14"
## [15] "15" "16" "17" "18" "19"
#view number of occurances per factor level
model_ms %>%
group_by(ms_label) %>%
summarise(no_rows = length(ms_label)) #cluster 1 has 5453 data points, 2-19 have one point each.
## # A tibble: 19 x 2
##    ms_label no_rows
##      <fctr>   <int>
##  1        1    5453
##  2        2       1
##  3        3       1
##  4        4       1
##  5        5       1
##  6        6       1
##  7        7       1
##  8        8       1
##  9        9       1
## 10       10       1
## 11       11       1
## 12       12       1
## 13       13       1
## 14       14       1
## 15       15       1
## 16       16       1
## 17       17       1
## 18       18       1
## 19       19       1
#plot using principal component anlaysis to reduce high-dimensional data to two dimensions
autoplot(
prcomp(model_ms[, 3:12], center = TRUE, scale. = TRUE),
data = model_ms,
colour = 'ms_label',
frame = TRUE
)

#H = 50.0
#MeanShift clustering using multi-core processing
options(mc.cores = 2)
ms_clustering <-
msClustering(model_df_trans, h = 50.0, multi.core = TRUE)

#attach clustering labels to model df
model_ms <- model_df
model_ms[, 'ms_label'] <- ms_clustering[2]

#change labels to factors
model_ms[, 'ms_label'] <- as.factor(model_ms[, 'ms_label'])

#view factor levels of ms_label column
levels(model_ms$ms_label)
## [1] "1" "2" "3" "4" "5" "6" "7" "8" "9"
#view number of occurances per factor level
model_ms %>%
group_by(ms_label) %>%
summarise(no_rows = length(ms_label)) #cluster 1 has 5463 data points, 2-9 have one point each.
## # A tibble: 9 x 2
##   ms_label no_rows
##     <fctr>   <int>
## 1        1    5463
## 2        2       1
## 3        3       1
## 4        4       1
## 5        5       1
## 6        6       1
## 7        7       1
## 8        8       1
## 9        9       1
#plot using principal component anlaysis to reduce high-dimensional data to two dimensions
autoplot(
prcomp(model_ms[, 3:12], center = TRUE, scale. = TRUE),
data = model_ms,
colour = 'ms_label',
frame = TRUE
)

#H = 75.0
#MeanShift clustering using multi-core processing
options(mc.cores = 2)
ms_clustering <-
msClustering(model_df_trans, h = 75.0, multi.core = TRUE)

#attach clustering labels to model df
model_ms <- model_df
model_ms[, 'ms_label'] <- ms_clustering[2]

#change labels to factors
model_ms[, 'ms_label'] <- as.factor(model_ms[, 'ms_label'])

#view factor levels of ms_label column
levels(model_ms$ms_label)
## [1] "1" "2" "3" "4"
#view number of occurances per factor level
model_ms %>%
group_by(ms_label) %>%
summarise(no_rows = length(ms_label)) #cluster 1 has 5468 data points, 2-4 have one point each.
## # A tibble: 4 x 2
##   ms_label no_rows
##     <fctr>   <int>
## 1        1    5468
## 2        2       1
## 3        3       1
## 4        4       1
#plot using principal component anlaysis to reduce high-dimensional data to two dimensions
autoplot(
prcomp(model_ms[, 3:12], center = TRUE, scale. = TRUE),
data = model_ms,
colour = 'ms_label',
frame = TRUE
)

Best Model with hyperparameter of h=20

It appears that using h of 20 resulted in a reasonable model. It clustered the data points into 1 primary cluster with 22 anomalies.

#H = 20.0
#MeanShift clustering using multi-core processing
options(mc.cores = 2)
ms_clustering <-
msClustering(model_df_trans, h = 20.0, multi.core = TRUE)

#attach clustering labels to model df
model_ms <- model_df
model_ms[, 'Cluster'] <- ms_clustering[2]

#change labels to factors
model_ms[, 'Cluster'] <- as.factor(model_ms[, 'Cluster'])

#view factor levels of ms_label column
levels(model_ms$Cluster)
##  [1] "1"  "2"  "3"  "4"  "5"  "6"  "7"  "8"  "9"  "10" "11" "12" "13" "14"
## [15] "15" "16" "17" "18" "19" "20" "21" "22" "23"
#view number of occurances per factor level
model_ms %>%
group_by(Cluster) %>%
summarise(no_rows = length(Cluster)) #cluster 1 has 5449 data points, clusters 2-23 have one point each.
## # A tibble: 23 x 2
##    Cluster no_rows
##     <fctr>   <int>
##  1       1    5449
##  2       2       1
##  3       3       1
##  4       4       1
##  5       5       1
##  6       6       1
##  7       7       1
##  8       8       1
##  9       9       1
## 10      10       1
## # ... with 13 more rows
#principal component anlaysis to reduce high-dimensional data to two dimensions
fraud_PCA <- prcomp(model_ms[, 3:12], center = TRUE, scale. = TRUE)
fraud_PCA2 <- fraud_PCA$x[, 1:2]

#plot cluster 1 add anomalies as crosses.
plot(
fraud_PCA2,
main = "Credit Card Transaction Clusters",
sub = "Anomalies plotted as circles with red crosses",
cex.sub = 0.75,
font.sub = 3,
col.sub = "red"
)
points(fraud_PCA2[model_ms$Cluster != 1, ], pch = 4, col = "red")

Anomalies

#create DF that include possible fraud transactions
fraud <- model_df[model_ms$Cluster != 1,]
fraud <- fraud[, 1:2]

#view fraud
kable(fraud) %>% kable_styling(latex_options = "scale_down")
Agency_Name Merchant_Category
35 ARDMORE HIGHER EDUCATION CENTER HOUSEHOLD APPLIANCE STORES
279 COMM. ON CONSUMER CREDIT GOVERNMENT SERVICES–NOT ELSEWHERE CLASSIFIED
293 COMM. ON CONSUMER CREDIT SHERATON
327 COMPSOURCE OKLAHOMA DELTA
1328 DEPARTMENT OF REHABILITATION SERVICES MISCELLANEOUS FOOD STORES-CONV STRS AND SPECIALTY MKTS.
2159 GRAND RIVER DAM AUTH. COMMERCIAL EQUIPMENT, NOT ELSEWHERE CLASSIFIED
2165 GRAND RIVER DAM AUTH. COMPUTERS, COMPUTER PERIPHERAL EQUIPMENT, SOFTWARE
2174 GRAND RIVER DAM AUTH. DETECTIVE AGENCIES,PROTECTIVE AGENCIES,AND SECURITY SERVICES
2194 GRAND RIVER DAM AUTH. GOVERNMENT SERVICES–NOT ELSEWHERE CLASSIFIED
2614 MENTAL HEALTH AND SUBSTANCE ABUSE SERV. DEPARTMENT STORES
2687 MENTAL HEALTH AND SUBSTANCE ABUSE SERV. RENAISSANCE HOTELS
2713 N. E. OKLA. A & M COLLEGE AUTOMATED FUEL DISPENSER
2752 N. E. OKLA. A & M COLLEGE RECORD STORES
2782 OFFICE OF JUVENILE AFFAIRS COMFORT HOTEL INTERNATIONAL
2975 OFFICE OF MANAGEMENT AND ENTERPRISE SERV TOLLS AND BRIDGE FEES
3330 OKLA. CITY COMMUNITY COLLEGE GROCERY STORES,AND SUPERMARKETS
3485 OKLA. PANHANDLE STATE UNIV. RECORD STORES
4165 REDLANDS COMMUNITY COLLEGE LUXOR HOTEL AND CASINO
4713 STATE DEPARTMENT OF HEALTH MISCELLANEOUS GENERAL MERCHANDISE
4717 STATE DEPARTMENT OF HEALTH NON-DURABLE GOODS NOT ELSEWHERE CLASSIFIED
4752 STATE ELECTION BOARD STATIONERY,OFFICE AND SCHOOL SUPPLY STORES
5156 UNIV.OF SCIENCE & ARTS OF OK COMFORT HOTEL INTERNATIONAL

Business Insight

Agency transactions that occurred within the merchant category listed in the fraud data frame could possibly be fraud based on my MeanShift analysis. Transactions that occurred within these merchant categories at these agencies require further analysis to determine if fraud actually occurred. Grand River Dam Auth had the highest number of merchant categories, 4, that might contain fraudulent transactions.

#Plot number of merchant categories that contain
#possible fraudulent transaactions by agency
ggplot(data = fraud, mapping = aes(Agency_Name)) + geom_bar(fill = 'blue', stat = "count") + xlab("Agency Name") + ylab("Number of Merchant Categories \nContaining Possible Fraudulent Transactions") + ggtitle("Possible Fraudulent Transactions") + coord_flip()

Autoencoder Modeling Technique

Autoencoder Method

Autoencoder is an unsupervised, neural network algorithm that uses backpropagation, setting the target values equal to the inputs. Autoencoders compress the input into a latent-space representation, and then reconstructs the output from this representation. It is typically used for dimension reduction.

Autoencoder Model

Hyperparameters tuned: Hidden layers: 5, 2, 5 and 10, 2, 10 Epochs: 50, 100, 200

#load libraries
library(h2o)
library(dplyr)
library(ggplot2)
h2o.init()
## 
## H2O is not running yet, starting it now...
## 
## Note:  In case of errors look at the following log files:
##     /var/folders/k6/qqdfd67942d5xb06yvglzqcr0000gn/T//RtmpxlEoPQ/h2o_meganroesch_started_from_r.out
##     /var/folders/k6/qqdfd67942d5xb06yvglzqcr0000gn/T//RtmpxlEoPQ/h2o_meganroesch_started_from_r.err
## 
## 
## Starting H2O JVM and connecting: .. Connection successful!
## 
## R is connected to the H2O cluster: 
##     H2O cluster uptime:         3 seconds 757 milliseconds 
##     H2O cluster timezone:       America/New_York 
##     H2O data parsing timezone:  UTC 
##     H2O cluster version:        3.20.0.2 
##     H2O cluster version age:    2 months and 7 days  
##     H2O cluster name:           H2O_started_from_R_meganroesch_gjo928 
##     H2O cluster total nodes:    1 
##     H2O cluster total memory:   3.56 GB 
##     H2O cluster total cores:    4 
##     H2O cluster allowed cores:  4 
##     H2O cluster healthy:        TRUE 
##     H2O Connection ip:          localhost 
##     H2O Connection port:        54321 
##     H2O Connection proxy:       NA 
##     H2O Internal Security:      FALSE 
##     H2O API Extensions:         XGBoost, Algos, AutoML, Core V3, Core V4 
##     R Version:                  R version 3.4.1 (2017-06-30)
# convert data to H2OFrame
model_h <- as.h2o(model_df_scale)
## 
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#view head of h20 model
kable(head(model_h))
Max_201307 Max_201308 Max_201309 Max_201310 Max_201311 Max_201312 Max_201401 Max_201402 Max_201403 Max_201404 Max_201405 Max_201406 Med_201307 Med_201308 Med_201309 Med_201310 Med_201311 Med_201312 Med_201401 Med_201402 Med_201403 Med_201404 Med_201405 Med_201406 MaxR_201307 MaxR_201308 MaxR_201309 MaxR_201310 MaxR_201311 MaxR_201312 MaxR_201401 MaxR_201402 MaxR_201403 MaxR_201404 MaxR_201405 MaxR_201406 MedR_201307 MedR_201308 MedR_201309 MedR_201310 MedR_201311 MedR_201312 MedR_201401 MedR_201402 MedR_201403 MedR_201404 MedR_201405 MedR_201406
0.0680335 -0.0248850 -0.3637536 -0.2787139 0.0135197 -0.3160999 0.7760440 -0.382932 -0.282552 -0.2563837 -0.3200084 -0.3912933 0.0764192 -0.1097998 -0.1824873 -0.1424242 -0.1040116 -0.0607806 0.4894809 -0.2397345 -0.225765 -0.0861667 -0.1588062 -0.1746778 -0.0822195 -0.0218471 -0.4295344 -0.454398 -0.4239034 -0.356182 1.5626181 -0.420211 -0.4670037 -0.4740046 -0.4624106 -0.4950477 0.7991785 1.0560317 -0.2099764 -0.2398453 -0.1999642 -0.1119167 1.4874624 -0.1204337 -0.1413479 -0.1252074 -0.1417702 -0.0967447
0.0877499 0.0126459 -0.3637536 -0.2787139 0.0135197 0.3290033 0.2536490 -0.382932 -0.282552 -0.2563837 -0.3200084 -0.3912933 0.1117813 0.1166292 -0.1824873 -0.1424242 -0.1040116 -0.0501229 0.0759417 -0.2397345 -0.225765 -0.0861667 -0.1588062 -0.1746778 2.7737374 -0.3783296 2.6082066 3.823477 5.0523924 -0.356182 -0.3954704 -0.420211 -0.4670037 -0.4740046 -0.4624106 -0.4950477 5.0890480 -0.2174755 -0.2099764 1.2078064 -0.1999642 -0.1119167 -0.0789986 -0.1204337 -0.1413479 -0.1252074 -0.1417702 -0.0967447
0.1829367 -0.0125401 -0.1284096 2.2689856 0.0135197 0.0492077 -0.1967417 -0.382932 -0.282552 -0.2563837 -0.3200084 -0.3912933 0.0423153 0.0545474 -0.0397959 0.2235111 -0.1040116 -0.0079566 -0.1019518 -0.2397345 -0.225765 -0.0861667 -0.1588062 -0.1746778 1.7840282 0.1865581 -0.4295344 3.950616 0.6432722 -0.356182 -0.3954704 -0.420211 -0.4670037 -0.4740046 -0.4624106 -0.4950477 18.6590433 3.7303969 -0.2099764 2.6554580 -0.1999642 -0.1119167 -0.0789986 -0.1204337 -0.1413479 -0.1252074 -0.1417702 -0.0967447
-0.0479014 0.0074599 -0.3637536 -0.2787139 0.0135197 0.7641744 0.6836222 -0.382932 -0.282552 -0.2563837 -0.3200084 -0.3912933 -0.1339843 -0.0893996 -0.1824873 -0.1424242 0.1135489 0.0403034 -0.0026706 -0.2397345 -0.225765 -0.0861667 -0.1588062 -0.1746778 -0.3053578 1.5023331 0.8022325 -0.454398 -0.4239034 1.931456 0.1618381 -0.420211 -0.4670037 -0.4740046 -0.4624106 -0.4950477 -0.3389502 1.5371345 0.2073472 -0.2398453 -0.1999642 0.8449992 0.0769432 -0.1204337 -0.1413479 -0.1252074 -0.1417702 -0.0967447
0.0364684 -0.0269110 -0.3637536 0.3158198 0.0135197 -0.3160999 -0.1967417 -0.382932 -0.282552 -0.2563837 -0.3200084 -0.3912933 0.0950119 -0.1291786 -0.1824873 0.0698889 -0.1040116 -0.0607806 -0.1019518 -0.2397345 -0.225765 -0.0861667 -0.1588062 -0.1746778 -0.3053578 -0.3783296 -0.4295344 1.019262 -0.4239034 -0.356182 -0.3954704 -0.420211 -0.4670037 -0.4740046 -0.4624106 -0.4950477 -0.3389502 -0.2174755 -0.2099764 0.4839806 -0.1999642 -0.1119167 -0.0789986 -0.1204337 -0.1413479 -0.1252074 -0.1417702 -0.0967447
-0.0147671 -0.0269110 1.1309317 1.5839023 0.0135197 0.1503852 -0.1570854 -0.382932 -0.282552 -0.2563837 -0.3200084 -0.3912933 -0.0322229 -0.1291786 0.1423728 0.1418943 -0.1040116 0.0007853 -0.0801584 -0.2397345 -0.225765 -0.0861667 -0.1588062 -0.1746778 -0.3053578 1.4148604 0.8288322 1.736543 -0.4239034 4.317895 -0.3954704 -0.420211 -0.4670037 -0.4740046 -0.4624106 -0.4950477 -0.3389502 0.2760086 0.5412060 0.4839806 -0.1999642 0.4007168 -0.0789986 -0.1204337 -0.1413479 -0.1252074 -0.1417702 -0.0967447 
#splitting the dataset into training and test sets
model_train_test <- h2o.splitFrame(model_h,
ratios = c(0.4, 0.4), # must add up to less than 1.0
seed = 42)

train  <- model_train_test[[1]]
test1  <- model_train_test[[2]]
test2  <- model_train_test[[3]]
dim(train)
## [1] 2184   48
dim(test1)
## [1] 2206   48
dim(test2)
## [1] 1081   48
#set features
x_col <- colnames(model_df_scale)

#Hyperparameters: hidden= 5,2,5 epochs = 100
#unsupervised neural network model using deep learning autoencoders (autoencoder = TRUE)
#“bottleneck” training, hidden layer in the middle is very small. Model will reduce the dimensionality of the input data (in this case, down to 2 nodes/dimensions).
model <- h2o.deeplearning(
x = x_col,
training_frame = train,
model_id = "model",
autoencoder = TRUE,
hidden = c(5, 2, 5),
epochs = 100,
activation = "Tanh"
)
## 
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#view model details
model
## Model Details:
## ==============
## 
## H2OAutoEncoderModel: deeplearning
## Model ID:  model 
## Status of Neuron Layers: auto-encoder, gaussian distribution, Quadratic loss, 560 weights/biases, 16.5 KB, 218,400 training samples, mini-batch size 1
##   layer units  type dropout       l1       l2 mean_rate rate_rms momentum
## 1     1    48 Input  0.00 %                                              
## 2     2     5  Tanh  0.00 % 0.000000 0.000000  0.521347 0.338643 0.000000
## 3     3     2  Tanh  0.00 % 0.000000 0.000000  0.038802 0.013525 0.000000
## 4     4     5  Tanh  0.00 % 0.000000 0.000000  0.019534 0.006614 0.000000
## 5     5    48  Tanh         0.000000 0.000000  0.024856 0.041152 0.000000
##   mean_weight weight_rms mean_bias bias_rms
## 1                                          
## 2   -0.083713   0.230006  0.226451 0.970561
## 3   -0.009294   0.579821  0.236353 0.115837
## 4   -0.240070   0.800421  0.009668 0.806640
## 5    0.006262   0.122727 -0.040154 0.056141
## 
## 
## H2OAutoEncoderMetrics: deeplearning
## ** Reported on training data. **
## 
## Training Set Metrics: 
## =====================
## 
## MSE: (Extract with `h2o.mse`) 0.002650377
## RMSE: (Extract with `h2o.rmse`) 0.05148181
#Test1
#dimensionality reduction to explore feature space
#extract this hidden feature and plot it to show the reduced #representation of the input data.
test1_col <-
h2o.deepfeatures(model, test1, layer = 2) %>% as.data.frame()
## 
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ggplot(test1_col, aes(x = DF.L2.C1, y = DF.L2.C2)) +
geom_point() #difficult to see outliers based on the graph

#use anomaly detection function

#anomaly detection
anomaly <- h2o.anomaly(model, test1) %>%
as.data.frame() %>%
tibble::rownames_to_column()

mean_mse <- anomaly %>%
summarise(mean = mean(Reconstruction.MSE))
mean_mse
##           mean
## 1 1.647652e+25
#plot
ggplot(anomaly, aes(x = as.numeric(rowname), y = Reconstruction.MSE)) +
geom_point(alpha = 0.3) +
geom_hline(data = mean_mse, aes(yintercept = mean)) +
scale_color_brewer(palette = "Set1")

#add outlier vs no outlier to anomaly df
anomaly <- anomaly %>%
mutate(outlier = ifelse(Reconstruction.MSE > 1.647652e+25, "outlier", "no_outlier"))

#subset which rows greater than mean mse
outlier <-
anomaly[which(anomaly[, 2] > 1.647652e+25), ] #row 1659 looks to be an anomaly

#plot
ggplot(anomaly, aes(x = as.numeric(rowname), y = Reconstruction.MSE)) +
geom_point(alpha = 0.3) +
geom_hline(data = mean_mse, aes(yintercept = mean)) +
scale_color_brewer(palette = "Set1") +
labs(x = "Row Number", y = "Reconstruction MSE") + geom_point(data = outlier, colour =
"red") +
geom_text(data = outlier,
label = "Anomaly",
vjust = 1)

#create DF that include possible fraud transactions row 1659 of test1 is equal to row 4165 of the model_df
fraud_auto <- model_df[4165, ]

#Test2
#dimensionality reduction to explore feature space
#extract this hidden feature and plot it to show the reduced #representation of the input data.
test2_col <-
h2o.deepfeatures(model, test2, layer = 2) %>% as.data.frame()
## 
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ggplot(test2_col, aes(x = DF.L2.C1, y = DF.L2.C2)) +
geom_point()

#anomaly detection
anomaly2 <- h2o.anomaly(model, test2) %>%
as.data.frame() %>%
tibble::rownames_to_column()

mean_mse <- anomaly2 %>%
summarise(mean = mean(Reconstruction.MSE))
mean_mse #0.007633034
##          mean
## 1 0.007556506
#plot
ggplot(anomaly2, aes(x = as.numeric(rowname), y = Reconstruction.MSE)) +
geom_point(alpha = 0.3) +
geom_hline(data = mean_mse, aes(yintercept = mean)) +
scale_color_brewer(palette = "Set1")

#add outlier vs no outlier to anomaly2 df
anomaly2 <- anomaly2 %>%
mutate(outlier = ifelse(Reconstruction.MSE > 0.25, "outlier", "no_outlier"))

#subset which rows greater than mean mse
outlier2 <-
anomaly2[which(anomaly2[, 2] > 0.25), ] #4 possible anomalies

#plot, possibly anomaly points are colored red
ggplot(anomaly2, aes(x = as.numeric(rowname), y = Reconstruction.MSE)) +
geom_point(alpha = 0.3) +
geom_hline(data = mean_mse, aes(yintercept = mean)) +
scale_color_brewer(palette = "Set1") +
labs(x = "Row Number", y = "Reconstruction MSE") + geom_point(data = outlier2, colour =
"red") + geom_text(data = outlier2,
label = "Anomaly",
vjust = 1)

#create DF that include possible fraud transactions
#row 532 of test2 is equal to row 2687 of the model_df
#row 537 of test2 is equal to row 2713 of the model_df
#row 589 of test2 is equal to row 573 of the model_df
#row 937 of test2 is equal to row 4752 of the model_df
fraud_auto2 <- model_df[c(2687, 2713, 573, 4752), ]
fraud_auto <- rbind(fraud_auto, fraud_auto2)

#Hyperparameters: hidden= 10,2,10 epochs = 100
model <- h2o.deeplearning(
x = x_col,
training_frame = train,
model_id = "model",
autoencoder = TRUE,
hidden = c(10, 2, 10),
epochs = 100,
activation = "Tanh"
)
## 
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#view model details
model
## Model Details:
## ==============
## 
## H2OAutoEncoderModel: deeplearning
## Model ID:  model 
## Status of Neuron Layers: auto-encoder, gaussian distribution, Quadratic loss, 1,070 weights/biases, 22.6 KB, 218,400 training samples, mini-batch size 1
##   layer units  type dropout       l1       l2 mean_rate rate_rms momentum
## 1     1    48 Input  0.00 %                                              
## 2     2    10  Tanh  0.00 % 0.000000 0.000000  0.277385 0.307664 0.000000
## 3     3     2  Tanh  0.00 % 0.000000 0.000000  0.012270 0.003171 0.000000
## 4     4    10  Tanh  0.00 % 0.000000 0.000000  0.011503 0.006643 0.000000
## 5     5    48  Tanh         0.000000 0.000000  0.015042 0.024994 0.000000
##   mean_weight weight_rms mean_bias bias_rms
## 1                                          
## 2   -0.015015   0.205557  0.178328 0.735836
## 3    0.185515   0.466652 -0.096877 0.300828
## 4    0.104532   0.606931 -0.105371 0.745774
## 5    0.005170   0.156369 -0.083767 0.171909
## 
## 
## H2OAutoEncoderMetrics: deeplearning
## ** Reported on training data. **
## 
## Training Set Metrics: 
## =====================
## 
## MSE: (Extract with `h2o.mse`) 0.002555075
## RMSE: (Extract with `h2o.rmse`) 0.05054775
#Test1
#dimensionality reduction to explore feature space
#extract this hidden feature and plot it to show the reduced #representation of the input data.
test1_col <-
h2o.deepfeatures(model, test1, layer = 2) %>% as.data.frame()
## 
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ggplot(test1_col, aes(x = DF.L2.C1, y = DF.L2.C2)) +
geom_point() #difficult to see which points are outliers, use anomaly detection

#anomaly detection
anomaly <- h2o.anomaly(model, test1) %>%
as.data.frame() %>%
tibble::rownames_to_column()

mean_mse <- anomaly %>%
summarise(mean = mean(Reconstruction.MSE))
mean_mse #1.647652e+25
##           mean
## 1 1.647652e+25
#plot
ggplot(anomaly, aes(x = as.numeric(rowname), y = Reconstruction.MSE)) +
geom_point(alpha = 0.3) +
geom_hline(data = mean_mse, aes(yintercept = mean)) +
scale_color_brewer(palette = "Set1")

#add outlier vs no outlier to anomaly df
anomaly <- anomaly %>%
mutate(outlier = ifelse(Reconstruction.MSE > 1.647652e+25, "outlier", "no_outlier"))

#subset which rows greater than mean mse
outlier <-
anomaly[which(anomaly[, 2] > 1.647652e+25), ] #again row 1659 looks to be an anomaly

#plot
ggplot(anomaly, aes(x = as.numeric(rowname), y = Reconstruction.MSE)) +
geom_point(alpha = 0.3) +
geom_hline(data = mean_mse, aes(yintercept = mean)) +
scale_color_brewer(palette = "Set1") +
labs(x = "Row Number", y = "Reconstruction MSE") + geom_point(data = outlier, colour =
"red") +
geom_text(data = outlier,
label = "Anomaly",
vjust = 1)

#create DF that include possible fraud transactions row 1659 of test1 is equal to row 4165 of the model_df
fraud_auto3 <- model_df[4165, ]

#Test2
#dimensionality reduction to explore feature space
#extract this hidden feature and plot it to show the reduced #representation of the input data.
test2_col <-
h2o.deepfeatures(model, test2, layer = 2) %>% as.data.frame()
## 
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  |                                                                       
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ggplot(test2_col, aes(x = DF.L2.C1, y = DF.L2.C2)) +
geom_point()  #difficult to see outliers, use anomaly detection function

#anomaly detection
anomaly2 <- h2o.anomaly(model, test2) %>%
as.data.frame() %>%
tibble::rownames_to_column()

mean_mse <- anomaly2 %>%
summarise(mean = mean(Reconstruction.MSE))
mean_mse #0.007471474
##          mean
## 1 0.007480511
#plot
ggplot(anomaly2, aes(x = as.numeric(rowname), y = Reconstruction.MSE)) +
geom_point(alpha = 0.3) +
geom_hline(data = mean_mse, aes(yintercept = mean)) +
scale_color_brewer(palette = "Set1")

#add outlier vs no outlier to anomaly2 df
anomaly2 <- anomaly2 %>%
mutate(outlier = ifelse(Reconstruction.MSE > 0.25, "outlier", "no_outlier"))

#subset which rows greater than mean mse
outlier2 <-
anomaly2[which(anomaly2[, 2] > 0.25), ] #again, 4 possible anomalies

#plot, possibly anomaly points are colored red
ggplot(anomaly2, aes(x = as.numeric(rowname), y = Reconstruction.MSE)) +
geom_point(alpha = 0.3) +
geom_hline(data = mean_mse, aes(yintercept = mean)) +
scale_color_brewer(palette = "Set1") +
labs(x = "Row Number", y = "Reconstruction MSE") + geom_point(data = outlier2, colour =
"red") + geom_text(data = outlier2,
label = "Anomaly",
vjust = 1)

#create DF that include possible fraud transactions
#row 532 of test2 is equal to row 2687 of the model_df
#row 537 of test2 is equal to row 2713 of the model_df
#row 589 of test2 is equal to row 573 of the model_df
#row 937 of test2 is equal to row 4752 of the model_df
fraud_auto4 <- model_df[c(2687, 2713, 573, 4752), ]
fraud_auto3 <- rbind(fraud_auto3, fraud_auto4)

#Hyperparameters: hidden= 5,2,5 epochs = 50
model <- h2o.deeplearning(
x = x_col,
training_frame = train,
model_id = "model",
autoencoder = TRUE,
hidden = c(5, 2, 5),
epochs = 50,
activation = "Tanh"
)
## 
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  |                                                                       
  |=================================================================| 100%
#view model details
model
## Model Details:
## ==============
## 
## H2OAutoEncoderModel: deeplearning
## Model ID:  model 
## Status of Neuron Layers: auto-encoder, gaussian distribution, Quadratic loss, 560 weights/biases, 16.5 KB, 109,200 training samples, mini-batch size 1
##   layer units  type dropout       l1       l2 mean_rate rate_rms momentum
## 1     1    48 Input  0.00 %                                              
## 2     2     5  Tanh  0.00 % 0.000000 0.000000  0.431818 0.305530 0.000000
## 3     3     2  Tanh  0.00 % 0.000000 0.000000  0.036133 0.016090 0.000000
## 4     4     5  Tanh  0.00 % 0.000000 0.000000  0.016816 0.005639 0.000000
## 5     5    48  Tanh         0.000000 0.000000  0.021853 0.031536 0.000000
##   mean_weight weight_rms mean_bias bias_rms
## 1                                          
## 2   -0.042468   0.195081  0.182341 0.497439
## 3   -0.282667   0.364345 -0.060672 0.202292
## 4    0.053229   0.638863  0.354854 0.205578
## 5    0.030075   0.145544 -0.014504 0.041839
## 
## 
## H2OAutoEncoderMetrics: deeplearning
## ** Reported on training data. **
## 
## Training Set Metrics: 
## =====================
## 
## MSE: (Extract with `h2o.mse`) 0.002688596
## RMSE: (Extract with `h2o.rmse`) 0.05185167
#Test1
#dimensionality reduction to explore feature space
#extract this hidden feature and plot it to show the reduced #representation of the input data.
test1_col <-
h2o.deepfeatures(model, test1, layer = 2) %>% as.data.frame()
## 
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ggplot(test1_col, aes(x = DF.L2.C1, y = DF.L2.C2)) +
geom_point() #difficult to see outliers, use anomaly detection function

#anomaly detection
anomaly <- h2o.anomaly(model, test1) %>%
as.data.frame() %>%
tibble::rownames_to_column()

mean_mse <- anomaly %>%
summarise(mean = mean(Reconstruction.MSE))
mean_mse #1.647652e+25
##           mean
## 1 1.647652e+25
#plot
ggplot(anomaly, aes(x = as.numeric(rowname), y = Reconstruction.MSE)) +
geom_point(alpha = 0.3) +
geom_hline(data = mean_mse, aes(yintercept = mean)) +
scale_color_brewer(palette = "Set1")

#add outlier vs no outlier to anomaly df
anomaly <- anomaly %>%
mutate(outlier = ifelse(Reconstruction.MSE > 1.647652e+25, "outlier", "no_outlier"))

#subset which rows greater than mean mse
outlier <-
anomaly[which(anomaly[, 2] > 1.647652e+25), ] #row 1659 looks to be an anomaly

#plot
ggplot(anomaly, aes(x = as.numeric(rowname), y = Reconstruction.MSE)) +
geom_point(alpha = 0.3) +
geom_hline(data = mean_mse, aes(yintercept = mean)) +
scale_color_brewer(palette = "Set1") +
labs(x = "Row Number", y = "Reconstruction MSE") + geom_point(data = outlier, colour =
"red") +
geom_text(data = outlier,
label = "Anomaly",
vjust = 1)

#create DF that include possible fraud transactions row 1659 of test1 is equal to row 4165 of the model_df
fraud_auto5 <- model_df[4165, ]

#Test2
#dimensionality reduction to explore feature space
#extract this hidden feature and plot it to show the reduced #representation of the input data.
test2_col <-
h2o.deepfeatures(model, test2, layer = 2) %>% as.data.frame()
## 
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  |                                                                 |   0%
  |                                                                       
  |=================================================================| 100%
ggplot(test2_col, aes(x = DF.L2.C1, y = DF.L2.C2)) +
geom_point() #difficult to see outliers, use anomaly function

#anomaly detection
anomaly2 <- h2o.anomaly(model, test2) %>%
as.data.frame() %>%
tibble::rownames_to_column()

mean_mse <- anomaly2 %>%
summarise(mean = mean(Reconstruction.MSE))
mean_mse #0.007654928
##          mean
## 1 0.007638525
#plot
ggplot(anomaly2, aes(x = as.numeric(rowname), y = Reconstruction.MSE)) +
geom_point(alpha = 0.3) +
geom_hline(data = mean_mse, aes(yintercept = mean)) +
scale_color_brewer(palette = "Set1")

#add outlier vs no outlier to anomaly2 df
anomaly2 <- anomaly2 %>%
mutate(outlier = ifelse(Reconstruction.MSE > 0.25, "outlier", "no_outlier"))

#subset which rows greater than mean mse
outlier2 <-
anomaly2[which(anomaly2[, 2] > 0.25), ] #4 possible anomalies

#plot, possibly anomaly points are colored red
ggplot(anomaly2, aes(x = as.numeric(rowname), y = Reconstruction.MSE)) +
geom_point(alpha = 0.3) +
geom_hline(data = mean_mse, aes(yintercept = mean)) +
scale_color_brewer(palette = "Set1") +
labs(x = "Row Number", y = "Reconstruction MSE") + geom_point(data = outlier2, colour =
"red") + geom_text(data = outlier2,
label = "Anomaly",
vjust = 1)

#create DF that include possible fraud transactions
#row 532 of test2 is equal to row 2687 of the model_df
#row 537 of test2 is equal to row 2713 of the model_df
#row 589 of test2 is equal to row 573 of the model_df
#row 937 of test2 is equal to row 4752 of the model_df
fraud_auto6 <- model_df[c(2687, 2713, 573, 4752), ]
fraud_auto5 <- rbind(fraud_auto5, fraud_auto5)

#Hyperparameters: hidden= 10,2,10 epochs = 50
model <- h2o.deeplearning(
x = x_col,
training_frame = train,
model_id = "model",
autoencoder = TRUE,
hidden = c(10, 2, 10),
epochs = 50,
activation = "Tanh"
)
## 
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  |                                                                       
  |====================================================             |  80%
  |                                                                       
  |=================================================================| 100%
#view model details
model
## Model Details:
## ==============
## 
## H2OAutoEncoderModel: deeplearning
## Model ID:  model 
## Status of Neuron Layers: auto-encoder, gaussian distribution, Quadratic loss, 1,070 weights/biases, 22.6 KB, 109,200 training samples, mini-batch size 1
##   layer units  type dropout       l1       l2 mean_rate rate_rms momentum
## 1     1    48 Input  0.00 %                                              
## 2     2    10  Tanh  0.00 % 0.000000 0.000000  0.461852 0.310685 0.000000
## 3     3     2  Tanh  0.00 % 0.000000 0.000000  0.041602 0.013158 0.000000
## 4     4    10  Tanh  0.00 % 0.000000 0.000000  0.011628 0.002403 0.000000
## 5     5    48  Tanh         0.000000 0.000000  0.035009 0.056452 0.000000
##   mean_weight weight_rms mean_bias bias_rms
## 1                                          
## 2    0.004638   0.199317  0.067262 0.493608
## 3    0.048928   0.334327 -0.018171 0.056111
## 4   -0.006798   0.460786  0.118686 0.297196
## 5    0.010035   0.160927 -0.015447 0.059579
## 
## 
## H2OAutoEncoderMetrics: deeplearning
## ** Reported on training data. **
## 
## Training Set Metrics: 
## =====================
## 
## MSE: (Extract with `h2o.mse`) 0.002695308
## RMSE: (Extract with `h2o.rmse`) 0.05191636
#Test1
#dimensionality reduction to explore feature space
#extract this hidden feature and plot it to show the reduced #representation of the input data.
test1_col <-
h2o.deepfeatures(model, test1, layer = 2) %>% as.data.frame()
## 
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  |                                                                       
  |=================================================================| 100%
ggplot(test1_col, aes(x = DF.L2.C1, y = DF.L2.C2)) +
geom_point() #difficult to see outliers, use anomaly function

#anomaly detection
anomaly <- h2o.anomaly(model, test1) %>%
as.data.frame() %>%
tibble::rownames_to_column()

mean_mse <- anomaly %>%
summarise(mean = mean(Reconstruction.MSE))
mean_mse #1.647652e+25
##           mean
## 1 1.647652e+25
#plot
ggplot(anomaly, aes(x = as.numeric(rowname), y = Reconstruction.MSE)) +
geom_point(alpha = 0.3) +
geom_hline(data = mean_mse, aes(yintercept = mean)) +
scale_color_brewer(palette = "Set1")

#add outlier vs no outlier to anomaly df
anomaly <- anomaly %>%
mutate(outlier = ifelse(Reconstruction.MSE > 1.647652e+25, "outlier", "no_outlier"))

#subset which rows greater than mean mse
outlier <-
anomaly[which(anomaly[, 2] > 1.647652e+25), ] #row 1659 looks to be an anomaly

#plot
ggplot(anomaly, aes(x = as.numeric(rowname), y = Reconstruction.MSE)) +
geom_point(alpha = 0.3) +
geom_hline(data = mean_mse, aes(yintercept = mean)) +
scale_color_brewer(palette = "Set1") +
labs(x = "Row Number", y = "Reconstruction MSE") + geom_point(data = outlier, colour =
"red") +
geom_text(data = outlier,
label = "Anomaly",
vjust = 1)

#create DF that include possible fraud transactions row 1659 of test1 is equal to row 4165 of the model_df
fraud_auto7 <- model_df[4165, ]

#Test2
#dimensionality reduction to explore feature space
#extract this hidden feature and plot it to show the reduced #representation of the input data.
test2_col <-
h2o.deepfeatures(model, test2, layer = 2) %>% as.data.frame()
## 
  |                                                                       
  |                                                                 |   0%
  |                                                                       
  |=================================================================| 100%
ggplot(test2_col, aes(x = DF.L2.C1, y = DF.L2.C2)) +
geom_point() #difficult to see outliers, use anomaly function

#anomaly detection
anomaly2 <- h2o.anomaly(model, test2) %>%
as.data.frame() %>%
tibble::rownames_to_column()

mean_mse <- anomaly2 %>%
summarise(mean = mean(Reconstruction.MSE))
mean_mse #0.007580477
##          mean
## 1 0.007654478
#plot
ggplot(anomaly2, aes(x = as.numeric(rowname), y = Reconstruction.MSE)) +
geom_point(alpha = 0.3) +
geom_hline(data = mean_mse, aes(yintercept = mean)) +
scale_color_brewer(palette = "Set1")

#add outlier vs no outlier to anomaly2 df
anomaly2 <- anomaly2 %>%
mutate(outlier = ifelse(Reconstruction.MSE > 0.25, "outlier", "no_outlier"))

#subset which rows greater than mean mse
outlier2 <-
anomaly2[which(anomaly2[, 2] > 0.25), ] #4 possible anomalies

#plot, possibly anomaly points are colored red
ggplot(anomaly2, aes(x = as.numeric(rowname), y = Reconstruction.MSE)) +
geom_point(alpha = 0.3) +
geom_hline(data = mean_mse, aes(yintercept = mean)) +
scale_color_brewer(palette = "Set1") +
labs(x = "Row Number", y = "Reconstruction MSE") + geom_point(data = outlier2, colour =
"red") + geom_text(data = outlier2,
label = "Anomaly",
vjust = 1)

#create DF that include possible fraud transactions
#row 532 of test2 is equal to row 2687 of the model_df
#row 537 of test2 is equal to row 2713 of the model_df
#row 589 of test2 is equal to row 573 of the model_df
#row 937 of test2 is equal to row 4752 of the model_df
fraud_auto8 <- model_df[c(2687, 2713, 573, 4752), ]
fraud_auto7 <- rbind(fraud_auto7, fraud_auto8)

#Hyperparameters: hidden= 5,2,5 epochs = 200
model <- h2o.deeplearning(
x = x_col,
training_frame = train,
model_id = "model",
autoencoder = TRUE,
hidden = c(5, 2, 5),
epochs = 200,
activation = "Tanh"
)
## 
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  |                                                                       
  |==========================================================       |  90%
  |                                                                       
  |=================================================================| 100%
#view model details
model
## Model Details:
## ==============
## 
## H2OAutoEncoderModel: deeplearning
## Model ID:  model 
## Status of Neuron Layers: auto-encoder, gaussian distribution, Quadratic loss, 560 weights/biases, 16.5 KB, 436,800 training samples, mini-batch size 1
##   layer units  type dropout       l1       l2 mean_rate rate_rms momentum
## 1     1    48 Input  0.00 %                                              
## 2     2     5  Tanh  0.00 % 0.000000 0.000000  0.647445 0.339183 0.000000
## 3     3     2  Tanh  0.00 % 0.000000 0.000000  0.031419 0.020157 0.000000
## 4     4     5  Tanh  0.00 % 0.000000 0.000000  0.021343 0.007451 0.000000
## 5     5    48  Tanh         0.000000 0.000000  0.015609 0.027358 0.000000
##   mean_weight weight_rms mean_bias bias_rms
## 1                                          
## 2    0.089554   0.236167 -0.698669 0.968084
## 3   -0.004764   0.729381  0.232981 0.304356
## 4    0.587888   0.754158 -0.968423 0.921102
## 5   -0.031601   0.132699 -0.105433 0.133616
## 
## 
## H2OAutoEncoderMetrics: deeplearning
## ** Reported on training data. **
## 
## Training Set Metrics: 
## =====================
## 
## MSE: (Extract with `h2o.mse`) 0.002673703
## RMSE: (Extract with `h2o.rmse`) 0.05170786
#Test1
#dimensionality reduction to explore feature space
#extract this hidden feature and plot it to show the reduced #representation of the input data.
test1_col <-
h2o.deepfeatures(model, test1, layer = 2) %>% as.data.frame()
## 
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  |================================                                 |  50%
  |                                                                       
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ggplot(test1_col, aes(x = DF.L2.C1, y = DF.L2.C2)) +
geom_point() #hard to see outliers, use anomaly detection

#anomaly detection
anomaly <- h2o.anomaly(model, test1) %>%
as.data.frame() %>%
tibble::rownames_to_column()

mean_mse <- anomaly %>%
summarise(mean = mean(Reconstruction.MSE))
mean_mse #1.647652e+25
##           mean
## 1 1.647652e+25
#plot
ggplot(anomaly, aes(x = as.numeric(rowname), y = Reconstruction.MSE)) +
geom_point(alpha = 0.3) +
geom_hline(data = mean_mse, aes(yintercept = mean)) +
scale_color_brewer(palette = "Set1")

#add outlier vs no outlier to anomaly df
anomaly <- anomaly %>%
mutate(outlier = ifelse(Reconstruction.MSE > 1.647652e+25, "outlier", "no_outlier"))

#subset which rows greater than mean mse
outlier <-
anomaly[which(anomaly[, 2] > 1.647652e+25), ] #row 1659 looks to be an anomaly

#plot
ggplot(anomaly, aes(x = as.numeric(rowname), y = Reconstruction.MSE)) +
geom_point(alpha = 0.3) +
geom_hline(data = mean_mse, aes(yintercept = mean)) +
scale_color_brewer(palette = "Set1") +
labs(x = "Row Number", y = "Reconstruction MSE") + geom_point(data = outlier, colour =
"red") +
geom_text(data = outlier,
label = "Anomaly",
vjust = 1)

#create DF that include possible fraud transactions row 1659 of test1 is equal to row 4165 of the model_df
fraud_auto9 <- model_df[4165, ]

#Test2
#dimensionality reduction to explore feature space
#extract this hidden feature and plot it to show the reduced #representation of the input data.
test2_col <-
h2o.deepfeatures(model, test2, layer = 2) %>% as.data.frame()
## 
  |                                                                       
  |                                                                 |   0%
  |                                                                       
  |=================================================================| 100%
ggplot(test2_col, aes(x = DF.L2.C1, y = DF.L2.C2)) +
geom_point() #difficult to see outliers, use anomaly detection function

#anomaly detection
anomaly2 <- h2o.anomaly(model, test2) %>%
as.data.frame() %>%
tibble::rownames_to_column()

mean_mse <- anomaly2 %>%
summarise(mean = mean(Reconstruction.MSE))
mean_mse #0.007565647
##          mean
## 1 0.007585463
#plot
ggplot(anomaly2, aes(x = as.numeric(rowname), y = Reconstruction.MSE)) +
geom_point(alpha = 0.3) +
geom_hline(data = mean_mse, aes(yintercept = mean)) +
scale_color_brewer(palette = "Set1")

#add outlier vs no outlier to anomaly2 df
anomaly2 <- anomaly2 %>%
mutate(outlier = ifelse(Reconstruction.MSE > 0.25, "outlier", "no_outlier"))

#subset which rows greater than mean mse
outlier2 <-
anomaly2[which(anomaly2[, 2] > 0.25), ] #4 possible anomalies

#plot, possibly anomaly points are colored red
ggplot(anomaly2, aes(x = as.numeric(rowname), y = Reconstruction.MSE)) +
geom_point(alpha = 0.3) +
geom_hline(data = mean_mse, aes(yintercept = mean)) +
scale_color_brewer(palette = "Set1") +
labs(x = "Row Number", y = "Reconstruction MSE") + geom_point(data = outlier2, colour =
"red") + geom_text(data = outlier2,
label = "Anomaly",
vjust = 1)

#create DF that include possible fraud transactions
#row 532 of test2 is equal to row 2687 of the model_df
#row 537 of test2 is equal to row 2713 of the model_df
#row 589 of test2 is equal to row 573 of the model_df
#row 937 of test2 is equal to row 4752 of the model_df
fraud_auto10 <- model_df[c(2687, 2713, 573, 4752), ]
fraud_auto9 <- rbind(fraud_auto9, fraud_auto10)

#Hyperparameters: hidden= 10,2,10 epochs = 200
#unsupervised neural network model using deep learning autoencoders (autoencoder = TRUE)
#“bottleneck” training, hidden layer in the middle is very small. Model will reduce the dimensionality of the input data (in this case, down to 2 nodes/dimensions).
model <- h2o.deeplearning(
x = x_col,
training_frame = train,
model_id = "model",
autoencoder = TRUE,
hidden = c(10, 2, 10),
epochs = 200,
activation = "Tanh"
)
## 
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  |                                                                       
  |==========================                                       |  40%
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  |=======================================                          |  60%
  |                                                                       
  |====================================================             |  80%
  |                                                                       
  |==============================================================   |  95%
  |                                                                       
  |=================================================================| 100%
#view model details
model
## Model Details:
## ==============
## 
## H2OAutoEncoderModel: deeplearning
## Model ID:  model 
## Status of Neuron Layers: auto-encoder, gaussian distribution, Quadratic loss, 1,070 weights/biases, 22.6 KB, 436,800 training samples, mini-batch size 1
##   layer units  type dropout       l1       l2 mean_rate rate_rms momentum
## 1     1    48 Input  0.00 %                                              
## 2     2    10  Tanh  0.00 % 0.000000 0.000000  0.453684 0.340695 0.000000
## 3     3     2  Tanh  0.00 % 0.000000 0.000000  0.020535 0.012176 0.000000
## 4     4    10  Tanh  0.00 % 0.000000 0.000000  0.028887 0.023118 0.000000
## 5     5    48  Tanh         0.000000 0.000000  0.015156 0.031581 0.000000
##   mean_weight weight_rms mean_bias bias_rms
## 1                                          
## 2   -0.039354   0.246624  0.206902 0.887383
## 3    0.177691   0.465519 -0.046751 0.053148
## 4    0.154542   0.838174 -0.084232 1.084916
## 5   -0.003295   0.138534 -0.116243 0.147573
## 
## 
## H2OAutoEncoderMetrics: deeplearning
## ** Reported on training data. **
## 
## Training Set Metrics: 
## =====================
## 
## MSE: (Extract with `h2o.mse`) 0.002489549
## RMSE: (Extract with `h2o.rmse`) 0.04989538
#Test1
#dimensionality reduction to explore feature space
#extract this hidden feature and plot it to show the reduced #representation of the input data.
test1_col <-
h2o.deepfeatures(model, test1, layer = 2) %>% as.data.frame()
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ggplot(test1_col, aes(x = DF.L2.C1, y = DF.L2.C2)) +
geom_point() #difficult to see outliers, use anomaly detection function

#anomaly detection
anomaly <- h2o.anomaly(model, test1) %>%
as.data.frame() %>%
tibble::rownames_to_column()

mean_mse <- anomaly %>%
summarise(mean = mean(Reconstruction.MSE))
mean_mse #1.647652e+25
##           mean
## 1 1.647652e+25
#plot
ggplot(anomaly, aes(x = as.numeric(rowname), y = Reconstruction.MSE)) +
geom_point(alpha = 0.3) +
geom_hline(data = mean_mse, aes(yintercept = mean)) +
scale_color_brewer(palette = "Set1")

#add outlier vs no outlier to anomaly df
anomaly <- anomaly %>%
mutate(outlier = ifelse(Reconstruction.MSE > 1.647652e+25, "outlier", "no_outlier"))

#subset which rows greater than mean mse
outlier <-
anomaly[which(anomaly[, 2] > 1.647652e+25), ] #row 1659 looks to be an anomaly

#plot
ggplot(anomaly, aes(x = as.numeric(rowname), y = Reconstruction.MSE)) +
geom_point(alpha = 0.3) +
geom_hline(data = mean_mse, aes(yintercept = mean)) +
scale_color_brewer(palette = "Set1") +
labs(x = "Row Number", y = "Reconstruction MSE") + geom_point(data = outlier, colour =
"red") +
geom_text(data = outlier,
label = "Anomaly",
vjust = 1)

#create DF that include possible fraud transactions row 1659 of test1 is equal to row 4165 of the model_df
fraud_auto11 <- model_df[4165, ]

#Test2
#dimensionality reduction to explore feature space
#extract this hidden feature and plot it to show the reduced #representation of the input data.
test2_col <-
h2o.deepfeatures(model, test2, layer = 2) %>% as.data.frame()
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ggplot(test2_col, aes(x = DF.L2.C1, y = DF.L2.C2)) +
geom_point() #difficult to see outliers, use anomaly detection function

#anomaly detection
anomaly2 <- h2o.anomaly(model, test2) %>%
as.data.frame() %>%
tibble::rownames_to_column()

mean_mse <- anomaly2 %>%
summarise(mean = mean(Reconstruction.MSE))
mean_mse #0.007465285
##          mean
## 1 0.007415878
#plot
ggplot(anomaly2, aes(x = as.numeric(rowname), y = Reconstruction.MSE)) +
geom_point(alpha = 0.3) +
geom_hline(data = mean_mse, aes(yintercept = mean)) +
scale_color_brewer(palette = "Set1")

#add outlier vs no outlier to anomaly2 df
anomaly2 <- anomaly2 %>%
mutate(outlier = ifelse(Reconstruction.MSE > 0.25, "outlier", "no_outlier"))

#subset which rows greater than mean mse
outlier2 <-
anomaly2[which(anomaly2[, 2] > 0.25), ] #4 possible anomalies

#plot, possibly anomaly points are colored red
ggplot(anomaly2, aes(x = as.numeric(rowname), y = Reconstruction.MSE)) +
geom_point(alpha = 0.3) +
geom_hline(data = mean_mse, aes(yintercept = mean)) +
scale_color_brewer(palette = "Set1") +
labs(x = "Row Number", y = "Reconstruction MSE") + geom_point(data = outlier2, colour =
"red") + geom_text(data = outlier2,
label = "Anomaly",
vjust = 1)

#create DF that include possible fraud transactions
#row 532 of test2 is equal to row 2687 of the model_df
#row 537 of test2 is equal to row 2713 of the model_df
#row 589 of test2 is equal to row 573 of the model_df
#row 937 of test2 is equal to row 4752 of the model_df
fraud_auto12 <- model_df[c(2687, 2713, 573, 4752), ]
fraud_auto11 <- rbind(fraud_auto11, fraud_auto12)

Anomalies

#all versions of tuned hyperparameters resulted in the same outliers
#view fraud_auto dataframe
kable(fraud_auto) %>% kable_styling(latex_options = "scale_down")
Agency_Name Merchant_Category Max_201307 Max_201308 Max_201309 Max_201310 Max_201311 Max_201312 Max_201401 Max_201402 Max_201403 Max_201404 Max_201405 Max_201406 Mean_201307 Mean_201308 Mean_201309 Mean_201310 Mean_201311 Mean_201312 Mean_201401 Mean_201402 Mean_201403 Mean_201404 Mean_201405 Mean_201406 Med_201307 Med_201308 Med_201309 Med_201310 Med_201311 Med_201312 Med_201401 Med_201402 Med_201403 Med_201404 Med_201405 Med_201406 MaxR_201307 MaxR_201308 MaxR_201309 MaxR_201310 MaxR_201311 MaxR_201312 MaxR_201401 MaxR_201402 MaxR_201403 MaxR_201404 MaxR_201405 MaxR_201406 MeanR_201307 MeanR_201308 MeanR_201309 MeanR_201310 MeanR_201311 MeanR_201312 MeanR_201401 MeanR_201402 MeanR_201403 MeanR_201404 MeanR_201405 MeanR_201406 MedR_201307 MedR_201308 MedR_201309 MedR_201310 MedR_201311 MedR_201312 MedR_201401 MedR_201402 MedR_201403 MedR_201404 MedR_201405 MedR_201406
4165 REDLANDS COMMUNITY COLLEGE LUXOR HOTEL AND CASINO 0.000000 0.000000 0.000000 0.000000 -2.421811e+16 0.0000000 0 0 0 0 0.0000000 0.0000000 0.000000 0.000000 0.0000000 0.000000 1.0000000 0.0000000 0 0 0 0 0.0000000 0.0000000 0.00000 0.000000 0.0000000 0.0000000 1.0000000 0.0000000 0 0 0 0 0.00 0.0000000 0 0.000000 0.000000 0.00 2 0.000000 0.000000 0.000000 0 0 0.000000 0.000000 0 0.0000 0.000 0.0 1 0.000 0.0 0.000 0 0 0.0 0.0 0 0.0 0 0 1 0.00 0 0 0 0 0.000000 0.0000000
2687 MENTAL HEALTH AND SUBSTANCE ABUSE SERV. RENAISSANCE HOTELS 1.773986 1.656732 0.000000 0.000000 7.434916e-01 2.9160310 0 0 0 0 0.0000000 0.0000000 1.773986 1.656732 0.0000000 0.000000 0.7434916 2.9160314 0 0 0 0 0.0000000 0.0000000 1.42751 1.333156 0.0000000 0.0000000 0.5982806 2.3465029 0 0 0 0 0.00 0.0000000 0 2.264151 1.509434 0.00 0 1.283019 0.000000 4.603774 0 0 0.000000 0.000000 0 0.0625 0.375 0.0 0 0.125 0.0 0.375 0 0 0.0 0.0 0 60.0 6 0 0 17.00 0 0 0 0 0.000000 0.0000000
2713 N. E. OKLA. A & M COLLEGE AUTOMATED FUEL DISPENSER 0.000000 0.000000 1.234737 1.349614 0.000000e+00 0.4567655 0 0 0 0 0.0000000 0.0000000 0.000000 0.000000 1.1525040 1.119113 0.0000000 0.4567655 0 0 0 0 0.0000000 0.0000000 0.00000 0.000000 1.0768340 1.0456345 0.0000000 0.4267753 0 0 0 0 0.00 0.0000000 0 0.000000 0.000000 0.05 0 3.950000 0.000000 0.000000 0 0 0.000000 0.000000 0 0.0000 0.250 0.5 0 0.250 0.0 0.000 0 0 0.0 0.0 0 0.0 0 1 0 158.00 0 0 0 0 0.000000 0.0000000
573 DEPARTMENT OF AGRICULTURE HOLIDAY INNS 0.000000 0.000000 1.657086 2.485629 1.181337e+00 3.7576390 0 0 0 0 0.0000000 0.0000000 0.000000 0.000000 0.8285429 1.059845 1.1813372 1.5486041 0 0 0 0 0.0000000 0.0000000 0.00000 0.000000 0.6666667 0.8916667 1.4258009 1.5158658 0 0 0 0 0.00 0.0000000 0 1.479290 3.846154 0.00 0 3.846154 3.106509 0.000000 0 0 0.000000 0.000000 0 0.3200 0.120 0.0 0 0.160 0.2 0.000 0 0 0.0 0.0 0 0.5 0 0 0 3.25 1 0 0 0 0.000000 0.0000000
4752 STATE ELECTION BOARD STATIONERY,OFFICE AND SCHOOL SUPPLY STORES 0.000000 0.000000 0.000000 0.000000 0.000000e+00 4.9158030 0 0 0 0 0.0748956 0.0050097 0.000000 0.000000 0.0000000 0.000000 0.0000000 4.9158030 0 0 0 0 0.0379237 0.0041748 0.00000 0.000000 0.0000000 0.0000000 0.0000000 981.2500000 0 0 0 0 7.57 0.8333333 0 0.000000 0.000000 0.00 0 0.000000 0.000000 0.000000 0 0 3.180723 0.313253 0 0.0000 0.000 0.0 0 0.000 0.0 0.000 0 0 0.5 0.5 0 0.0 0 0 0 0.00 0 0 0 0 4.606061 0.4242424

Business Insight

Agency transactions that occurred within the merchant category listed in the fraud_auto data frame could possibly be fraud based on my Autoencoder analysis. Transactions that occurred within these merchant categories at these agencies require further analysis to determine if fraud actually occurred.

Of the five agency transactions flagged as possible anomalies using Autoencoder, all but one was also flagged with my MeanShift model. The one data point that was flagged by Autoencoder but not MeanShift was the Holiday Inns category of the Department of Agriculture.

Overall, I found using Autoencoder more challenging for anomaly detection than MeanShift as the model did not cluster data points.

#Plot number of merchant categories that contain
#possible fraudulent transaactions by agency
ggplot(data = fraud_auto, mapping = aes(Agency_Name)) + geom_bar(fill = 'blue', stat = "count") + xlab("Agency Name") + ylab("Number of Merchant Categories \nContaining Possible Fraudulent Transactions") + ggtitle("Possible Fraudulent Transactions") + coord_flip()